Find the Function Rule table[[x,y],[2,15],[6,13],[7,9],[8,8],[12,5]]

$\begin{array}{c} x & y \\ 2 & 15 \\ 6 & 13 \\ 7 & 9 \\ 8 & 8 \\ 12 & 5 \end{array}$

Check if the function rule is linear.

To find if the table follows a function rule, check to see if the values follow the linear form $y = a x + b$ .

$y = a x + b$

Build a set of equations from the table such that $y = a x + b$ .

$15 = a (2) + b 13 = a (6) + b 9 = a (7) + b 8 = a (8) + b 5 = a (12) + b$

Calculate the values of $a$ and $b$ .

Solve for $b$ in $15 = a (2) + b$ .

Rewrite the equation as $a (2) + b = 15$ .

$a (2) + b = 15$

$13 = a (6) + b$

$9 = a (7) + b$

$8 = a (8) + b$

$5 = a (12) + b$

Move $2$ to the left of $a$ .

$2 a + b = 15$

$13 = a (6) + b$

$9 = a (7) + b$

$8 = a (8) + b$

$5 = a (12) + b$

Subtract $2 a$ from both sides of the equation.

$b = 15 - 2 a$

$13 = a (6) + b$

$9 = a (7) + b$

$8 = a (8) + b$

$5 = a (12) + b$

$b = 15 - 2 a$

$13 = a (6) + b$

$9 = a (7) + b$

$8 = a (8) + b$

$5 = a (12) + b$

Replace all occurrences of $b$ with $15 - 2 a$ in each equation.

Replace all occurrences of $b$ in $13 = a (6) + b$ with $15 - 2 a$ .

$13 = a (6) + 15 - 2 a$

$b = 15 - 2 a$

$9 = a (7) + b$

$8 = a (8) + b$

$5 = a (12) + b$

Simplify $13 = a (6) + 15 - 2 a$ .

Simplify the left side.

Remove parentheses.

$13 = a (6) + 15 - 2 a$

$b = 15 - 2 a$

$9 = a (7) + b$

$8 = a (8) + b$

$5 = a (12) + b$

$13 = a (6) + 15 - 2 a$

$b = 15 - 2 a$

$9 = a (7) + b$

$8 = a (8) + b$

$5 = a (12) + b$

Simplify the right side.

Simplify $a (6) + 15 - 2 a$ .

Move $6$ to the left of $a$ .

$13 = 6 a + 15 - 2 a$

$b = 15 - 2 a$

$9 = a (7) + b$

$8 = a (8) + b$

$5 = a (12) + b$

Subtract $2 a$ from $6 a$ .

$13 = 4 a + 15$

$b = 15 - 2 a$

$9 = a (7) + b$

$8 = a (8) + b$

$5 = a (12) + b$

$13 = 4 a + 15$

$b = 15 - 2 a$

$9 = a (7) + b$

$8 = a (8) + b$

$5 = a (12) + b$

$13 = 4 a + 15$

$b = 15 - 2 a$

$9 = a (7) + b$

$8 = a (8) + b$

$5 = a (12) + b$

$13 = 4 a + 15$

$b = 15 - 2 a$

$9 = a (7) + b$

$8 = a (8) + b$

$5 = a (12) + b$

Replace all occurrences of $b$ in $9 = a (7) + b$ with $15 - 2 a$ .

$9 = a (7) + 15 - 2 a$

$13 = 4 a + 15$

$b = 15 - 2 a$

$8 = a (8) + b$

$5 = a (12) + b$

Simplify $9 = a (7) + 15 - 2 a$ .

Simplify the left side.

Remove parentheses.

$9 = a (7) + 15 - 2 a$

$13 = 4 a + 15$

$b = 15 - 2 a$

$8 = a (8) + b$

$5 = a (12) + b$

$9 = a (7) + 15 - 2 a$

$13 = 4 a + 15$

$b = 15 - 2 a$

$8 = a (8) + b$

$5 = a (12) + b$

Simplify the right side.

Simplify $a (7) + 15 - 2 a$ .

Move $7$ to the left of $a$ .

$9 = 7 a + 15 - 2 a$

$13 = 4 a + 15$

$b = 15 - 2 a$

$8 = a (8) + b$

$5 = a (12) + b$

Subtract $2 a$ from $7 a$ .

$9 = 5 a + 15$

$13 = 4 a + 15$

$b = 15 - 2 a$

$8 = a (8) + b$

$5 = a (12) + b$

$9 = 5 a + 15$

$13 = 4 a + 15$

$b = 15 - 2 a$

$8 = a (8) + b$

$5 = a (12) + b$

$9 = 5 a + 15$

$13 = 4 a + 15$

$b = 15 - 2 a$

$8 = a (8) + b$

$5 = a (12) + b$

$9 = 5 a + 15$

$13 = 4 a + 15$

$b = 15 - 2 a$

$8 = a (8) + b$

$5 = a (12) + b$

Replace all occurrences of $b$ in $8 = a (8) + b$ with $15 - 2 a$ .

$8 = a (8) + 15 - 2 a$

$9 = 5 a + 15$

$13 = 4 a + 15$

$b = 15 - 2 a$

$5 = a (12) + b$

Simplify $8 = a (8) + 15 - 2 a$ .

Simplify the left side.

Remove parentheses.

$8 = a (8) + 15 - 2 a$

$9 = 5 a + 15$

$13 = 4 a + 15$

$b = 15 - 2 a$

$5 = a (12) + b$

$8 = a (8) + 15 - 2 a$

$9 = 5 a + 15$

$13 = 4 a + 15$

$b = 15 - 2 a$

$5 = a (12) + b$

Simplify the right side.

Simplify $a (8) + 15 - 2 a$ .

Move $8$ to the left of $a$ .

$8 = 8 a + 15 - 2 a$

$9 = 5 a + 15$

$13 = 4 a + 15$

$b = 15 - 2 a$

$5 = a (12) + b$

Subtract $2 a$ from $8 a$ .

$8 = 6 a + 15$

$9 = 5 a + 15$

$13 = 4 a + 15$

$b = 15 - 2 a$

$5 = a (12) + b$

$8 = 6 a + 15$

$9 = 5 a + 15$

$13 = 4 a + 15$

$b = 15 - 2 a$

$5 = a (12) + b$

$8 = 6 a + 15$

$9 = 5 a + 15$

$13 = 4 a + 15$

$b = 15 - 2 a$

$5 = a (12) + b$

$8 = 6 a + 15$

$9 = 5 a + 15$

$13 = 4 a + 15$

$b = 15 - 2 a$

$5 = a (12) + b$

Replace all occurrences of $b$ in $5 = a (12) + b$ with $15 - 2 a$ .

$5 = a (12) + 15 - 2 a$

$8 = 6 a + 15$

$9 = 5 a + 15$

$13 = 4 a + 15$

$b = 15 - 2 a$

Simplify $5 = a (12) + 15 - 2 a$ .

Simplify the left side.

Remove parentheses.

$5 = a (12) + 15 - 2 a$

$8 = 6 a + 15$

$9 = 5 a + 15$

$13 = 4 a + 15$

$b = 15 - 2 a$

$5 = a (12) + 15 - 2 a$

$8 = 6 a + 15$

$9 = 5 a + 15$

$13 = 4 a + 15$

$b = 15 - 2 a$

Simplify the right side.

Simplify $a (12) + 15 - 2 a$ .

Move $12$ to the left of $a$ .

$5 = 12 a + 15 - 2 a$

$8 = 6 a + 15$

$9 = 5 a + 15$

$13 = 4 a + 15$

$b = 15 - 2 a$

Subtract $2 a$ from $12 a$ .

$5 = 10 a + 15$

$8 = 6 a + 15$

$9 = 5 a + 15$

$13 = 4 a + 15$

$b = 15 - 2 a$

$5 = 10 a + 15$

$8 = 6 a + 15$

$9 = 5 a + 15$

$13 = 4 a + 15$

$b = 15 - 2 a$

$5 = 10 a + 15$

$8 = 6 a + 15$

$9 = 5 a + 15$

$13 = 4 a + 15$

$b = 15 - 2 a$

$5 = 10 a + 15$

$8 = 6 a + 15$

$9 = 5 a + 15$

$13 = 4 a + 15$

$b = 15 - 2 a$

$5 = 10 a + 15$

$8 = 6 a + 15$

$9 = 5 a + 15$

$13 = 4 a + 15$

$b = 15 - 2 a$

Solve for $a$ in $5 = 10 a + 15$ .

Rewrite the equation as $10 a + 15 = 5$ .

$10 a + 15 = 5$

$8 = 6 a + 15$

$9 = 5 a + 15$

$13 = 4 a + 15$

$b = 15 - 2 a$

Move all terms not containing $a$ to the right side of the equation.

Subtract $15$ from both sides of the equation.

$10 a = 5 - 15$

$8 = 6 a + 15$

$9 = 5 a + 15$

$13 = 4 a + 15$

$b = 15 - 2 a$

Subtract $15$ from $5$ .

$10 a = - 10$

$8 = 6 a + 15$

$9 = 5 a + 15$

$13 = 4 a + 15$

$b = 15 - 2 a$

$10 a = - 10$

$8 = 6 a + 15$

$9 = 5 a + 15$

$13 = 4 a + 15$

$b = 15 - 2 a$

Divide each term in $10 a = - 10$ by $10$ and simplify.

Divide each term in $10 a = - 10$ by $10$ .

$\frac{10 a}{10} = \frac{- 10}{10}$

$8 = 6 a + 15$

$9 = 5 a + 15$

$13 = 4 a + 15$

$b = 15 - 2 a$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 a}{10} = \frac{- 10}{10}$

$8 = 6 a + 15$

$9 = 5 a + 15$

$13 = 4 a + 15$

$b = 15 - 2 a$

Divide $a$ by $1$ .

$a = \frac{- 10}{10}$

$8 = 6 a + 15$

$9 = 5 a + 15$

$13 = 4 a + 15$

$b = 15 - 2 a$

$a = \frac{- 10}{10}$

$8 = 6 a + 15$

$9 = 5 a + 15$

$13 = 4 a + 15$

$b = 15 - 2 a$

$a = \frac{- 10}{10}$

$8 = 6 a + 15$

$9 = 5 a + 15$

$13 = 4 a + 15$

$b = 15 - 2 a$

Simplify the right side.

Divide $- 10$ by $10$ .

$a = - 1$

$8 = 6 a + 15$

$9 = 5 a + 15$

$13 = 4 a + 15$

$b = 15 - 2 a$

$a = - 1$

$8 = 6 a + 15$

$9 = 5 a + 15$

$13 = 4 a + 15$

$b = 15 - 2 a$

$a = - 1$

$8 = 6 a + 15$

$9 = 5 a + 15$

$13 = 4 a + 15$

$b = 15 - 2 a$

$a = - 1$

$8 = 6 a + 15$

$9 = 5 a + 15$

$13 = 4 a + 15$

$b = 15 - 2 a$

Replace all occurrences of $a$ with $- 1$ in each equation.

Replace all occurrences of $a$ in $8 = 6 a + 15$ with $- 1$ .

$8 = 6 (- 1) + 15$

$a = - 1$

$9 = 5 a + 15$

$13 = 4 a + 15$

$b = 15 - 2 a$

Simplify the right side.

Simplify $6 (- 1) + 15$ .

Multiply $6$ by $- 1$ .

$8 = - 6 + 15$

$a = - 1$

$9 = 5 a + 15$

$13 = 4 a + 15$

$b = 15 - 2 a$

Add $- 6$ and $15$ .

$8 = 9$

$a = - 1$

$9 = 5 a + 15$

$13 = 4 a + 15$

$b = 15 - 2 a$

$8 = 9$

$a = - 1$

$9 = 5 a + 15$

$13 = 4 a + 15$

$b = 15 - 2 a$

$8 = 9$

$a = - 1$

$9 = 5 a + 15$

$13 = 4 a + 15$

$b = 15 - 2 a$

Replace all occurrences of $a$ in $9 = 5 a + 15$ with $- 1$ .

$9 = 5 (- 1) + 15$

$8 = 9$

$a = - 1$

$13 = 4 a + 15$

$b = 15 - 2 a$

Simplify the right side.

Simplify $5 (- 1) + 15$ .

Multiply $5$ by $- 1$ .

$9 = - 5 + 15$

$8 = 9$

$a = - 1$

$13 = 4 a + 15$

$b = 15 - 2 a$

Add $- 5$ and $15$ .

$9 = 10$

$8 = 9$

$a = - 1$

$13 = 4 a + 15$

$b = 15 - 2 a$

$9 = 10$

$8 = 9$

$a = - 1$

$13 = 4 a + 15$

$b = 15 - 2 a$

$9 = 10$

$8 = 9$

$a = - 1$

$13 = 4 a + 15$

$b = 15 - 2 a$

Replace all occurrences of $a$ in $13 = 4 a + 15$ with $- 1$ .

$13 = 4 (- 1) + 15$

$9 = 10$

$8 = 9$

$a = - 1$

$b = 15 - 2 a$

Simplify the right side.

Simplify $4 (- 1) + 15$ .

Multiply $4$ by $- 1$ .

$13 = - 4 + 15$

$9 = 10$

$8 = 9$

$a = - 1$

$b = 15 - 2 a$

Add $- 4$ and $15$ .

$13 = 11$

$9 = 10$

$8 = 9$

$a = - 1$

$b = 15 - 2 a$

$13 = 11$

$9 = 10$

$8 = 9$

$a = - 1$

$b = 15 - 2 a$

$13 = 11$

$9 = 10$

$8 = 9$

$a = - 1$

$b = 15 - 2 a$

Replace all occurrences of $a$ in $b = 15 - 2 a$ with $- 1$ .

$b = 15 - 2 \cdot - 1$

$13 = 11$

$9 = 10$

$8 = 9$

$a = - 1$

Simplify the right side.

Simplify $15 - 2 \cdot - 1$ .

Multiply $- 2$ by $- 1$ .

$b = 15 + 2$

$13 = 11$

$9 = 10$

$8 = 9$

$a = - 1$

Add $15$ and $2$ .

$b = 17$

$13 = 11$

$9 = 10$

$8 = 9$

$a = - 1$

$b = 17$

$13 = 11$

$9 = 10$

$8 = 9$

$a = - 1$

$b = 17$

$13 = 11$

$9 = 10$

$8 = 9$

$a = - 1$

$b = 17$

$13 = 11$

$9 = 10$

$8 = 9$

$a = - 1$

Since $13 = 11$ is not true, there is no solution.

No solution

Since $y \neq y$ for the corresponding $x$ values, the function is not linear.

The function is not linear

Check if the function rule is quadratic.

To find if the table follows a function rule, check whether the function rule could follow the form $y = a x^{2} + b x + c$ .

$y = a x^{2} + b x + c$

Build a set of $3$ equations from the table such that $y = a x^{2} + b x + c$ .

Calculate the values of $a$ , $b$ , and $c$ .

Solve for $c$ in $15 = a \cdot 2^{2} + b (2) + c$ .

Rewrite the equation as $a \cdot 2^{2} + b (2) + c = 15$ .

$a \cdot 2^{2} + b (2) + c = 15$

$13 = a \cdot 6^{2} + b (6) + c$

$9 = a \cdot 7^{2} + b (7) + c$

$8 = a \cdot 8^{2} + b (8) + c$

$5 = a \cdot 12^{2} + b (12) + c$

Simplify each term.

Raise $2$ to the power of $2$ .

$a \cdot 4 + b (2) + c = 15$

$13 = a \cdot 6^{2} + b (6) + c$

$9 = a \cdot 7^{2} + b (7) + c$

$8 = a \cdot 8^{2} + b (8) + c$

$5 = a \cdot 12^{2} + b (12) + c$

Move $4$ to the left of $a$ .

$4 \cdot a + b (2) + c = 15$

$13 = a \cdot 6^{2} + b (6) + c$

$9 = a \cdot 7^{2} + b (7) + c$

$8 = a \cdot 8^{2} + b (8) + c$

$5 = a \cdot 12^{2} + b (12) + c$

Move $2$ to the left of $b$ .

$4 a + 2 b + c = 15$

$13 = a \cdot 6^{2} + b (6) + c$

$9 = a \cdot 7^{2} + b (7) + c$

$8 = a \cdot 8^{2} + b (8) + c$

$5 = a \cdot 12^{2} + b (12) + c$

$4 a + 2 b + c = 15$

$13 = a \cdot 6^{2} + b (6) + c$

$9 = a \cdot 7^{2} + b (7) + c$

$8 = a \cdot 8^{2} + b (8) + c$

$5 = a \cdot 12^{2} + b (12) + c$

Move all terms not containing $c$ to the right side of the equation.

Subtract $4 a$ from both sides of the equation.

$2 b + c = 15 - 4 a$

$13 = a \cdot 6^{2} + b (6) + c$

$9 = a \cdot 7^{2} + b (7) + c$

$8 = a \cdot 8^{2} + b (8) + c$

$5 = a \cdot 12^{2} + b (12) + c$

Subtract $2 b$ from both sides of the equation.

$c = 15 - 4 a - 2 b$

$13 = a \cdot 6^{2} + b (6) + c$

$9 = a \cdot 7^{2} + b (7) + c$

$8 = a \cdot 8^{2} + b (8) + c$

$5 = a \cdot 12^{2} + b (12) + c$

$c = 15 - 4 a - 2 b$

$13 = a \cdot 6^{2} + b (6) + c$

$9 = a \cdot 7^{2} + b (7) + c$

$8 = a \cdot 8^{2} + b (8) + c$

$5 = a \cdot 12^{2} + b (12) + c$

$c = 15 - 4 a - 2 b$

$13 = a \cdot 6^{2} + b (6) + c$

$9 = a \cdot 7^{2} + b (7) + c$

$8 = a \cdot 8^{2} + b (8) + c$

$5 = a \cdot 12^{2} + b (12) + c$

Replace all occurrences of $c$ with $15 - 4 a - 2 b$ in each equation.

Replace all occurrences of $c$ in $13 = a \cdot 6^{2} + b (6) + c$ with $15 - 4 a - 2 b$ .

$13 = a \cdot 6^{2} + b (6) + 15 - 4 a - 2 b$

$c = 15 - 4 a - 2 b$

$9 = a \cdot 7^{2} + b (7) + c$

$8 = a \cdot 8^{2} + b (8) + c$

$5 = a \cdot 12^{2} + b (12) + c$

Simplify $13 = a \cdot 6^{2} + b (6) + 15 - 4 a - 2 b$ .

Simplify the left side.

Remove parentheses.

$13 = a \cdot 6^{2} + b (6) + 15 - 4 a - 2 b$

$c = 15 - 4 a - 2 b$

$9 = a \cdot 7^{2} + b (7) + c$

$8 = a \cdot 8^{2} + b (8) + c$

$5 = a \cdot 12^{2} + b (12) + c$

$13 = a \cdot 6^{2} + b (6) + 15 - 4 a - 2 b$

$c = 15 - 4 a - 2 b$

$9 = a \cdot 7^{2} + b (7) + c$

$8 = a \cdot 8^{2} + b (8) + c$

$5 = a \cdot 12^{2} + b (12) + c$

Simplify the right side.

Simplify $a \cdot 6^{2} + b (6) + 15 - 4 a - 2 b$ .

Simplify each term.

Raise $6$ to the power of $2$ .

$13 = a \cdot 36 + b (6) + 15 - 4 a - 2 b$

$c = 15 - 4 a - 2 b$

$9 = a \cdot 7^{2} + b (7) + c$

$8 = a \cdot 8^{2} + b (8) + c$

$5 = a \cdot 12^{2} + b (12) + c$

Move $36$ to the left of $a$ .

$13 = 36 \cdot a + b (6) + 15 - 4 a - 2 b$

$c = 15 - 4 a - 2 b$

$9 = a \cdot 7^{2} + b (7) + c$

$8 = a \cdot 8^{2} + b (8) + c$

$5 = a \cdot 12^{2} + b (12) + c$

Move $6$ to the left of $b$ .

$13 = 36 a + 6 b + 15 - 4 a - 2 b$

$c = 15 - 4 a - 2 b$

$9 = a \cdot 7^{2} + b (7) + c$

$8 = a \cdot 8^{2} + b (8) + c$

$5 = a \cdot 12^{2} + b (12) + c$

$13 = 36 a + 6 b + 15 - 4 a - 2 b$

$c = 15 - 4 a - 2 b$

$9 = a \cdot 7^{2} + b (7) + c$

$8 = a \cdot 8^{2} + b (8) + c$

$5 = a \cdot 12^{2} + b (12) + c$

Simplify by adding terms.

Subtract $4 a$ from $36 a$ .

$13 = 32 a + 6 b + 15 - 2 b$

$c = 15 - 4 a - 2 b$

$9 = a \cdot 7^{2} + b (7) + c$

$8 = a \cdot 8^{2} + b (8) + c$

$5 = a \cdot 12^{2} + b (12) + c$

Subtract $2 b$ from $6 b$ .

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$9 = a \cdot 7^{2} + b (7) + c$

$8 = a \cdot 8^{2} + b (8) + c$

$5 = a \cdot 12^{2} + b (12) + c$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$9 = a \cdot 7^{2} + b (7) + c$

$8 = a \cdot 8^{2} + b (8) + c$

$5 = a \cdot 12^{2} + b (12) + c$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$9 = a \cdot 7^{2} + b (7) + c$

$8 = a \cdot 8^{2} + b (8) + c$

$5 = a \cdot 12^{2} + b (12) + c$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$9 = a \cdot 7^{2} + b (7) + c$

$8 = a \cdot 8^{2} + b (8) + c$

$5 = a \cdot 12^{2} + b (12) + c$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$9 = a \cdot 7^{2} + b (7) + c$

$8 = a \cdot 8^{2} + b (8) + c$

$5 = a \cdot 12^{2} + b (12) + c$

Replace all occurrences of $c$ in $9 = a \cdot 7^{2} + b (7) + c$ with $15 - 4 a - 2 b$ .

$9 = a \cdot 7^{2} + b (7) + 15 - 4 a - 2 b$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$8 = a \cdot 8^{2} + b (8) + c$

$5 = a \cdot 12^{2} + b (12) + c$

Simplify $9 = a \cdot 7^{2} + b (7) + 15 - 4 a - 2 b$ .

Simplify the left side.

Remove parentheses.

$9 = a \cdot 7^{2} + b (7) + 15 - 4 a - 2 b$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$8 = a \cdot 8^{2} + b (8) + c$

$5 = a \cdot 12^{2} + b (12) + c$

$9 = a \cdot 7^{2} + b (7) + 15 - 4 a - 2 b$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$8 = a \cdot 8^{2} + b (8) + c$

$5 = a \cdot 12^{2} + b (12) + c$

Simplify the right side.

Simplify $a \cdot 7^{2} + b (7) + 15 - 4 a - 2 b$ .

Simplify each term.

Raise $7$ to the power of $2$ .

$9 = a \cdot 49 + b (7) + 15 - 4 a - 2 b$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$8 = a \cdot 8^{2} + b (8) + c$

$5 = a \cdot 12^{2} + b (12) + c$

Move $49$ to the left of $a$ .

$9 = 49 \cdot a + b (7) + 15 - 4 a - 2 b$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$8 = a \cdot 8^{2} + b (8) + c$

$5 = a \cdot 12^{2} + b (12) + c$

Move $7$ to the left of $b$ .

$9 = 49 a + 7 b + 15 - 4 a - 2 b$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$8 = a \cdot 8^{2} + b (8) + c$

$5 = a \cdot 12^{2} + b (12) + c$

$9 = 49 a + 7 b + 15 - 4 a - 2 b$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$8 = a \cdot 8^{2} + b (8) + c$

$5 = a \cdot 12^{2} + b (12) + c$

Simplify by adding terms.

Subtract $4 a$ from $49 a$ .

$9 = 45 a + 7 b + 15 - 2 b$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$8 = a \cdot 8^{2} + b (8) + c$

$5 = a \cdot 12^{2} + b (12) + c$

Subtract $2 b$ from $7 b$ .

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$8 = a \cdot 8^{2} + b (8) + c$

$5 = a \cdot 12^{2} + b (12) + c$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$8 = a \cdot 8^{2} + b (8) + c$

$5 = a \cdot 12^{2} + b (12) + c$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$8 = a \cdot 8^{2} + b (8) + c$

$5 = a \cdot 12^{2} + b (12) + c$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$8 = a \cdot 8^{2} + b (8) + c$

$5 = a \cdot 12^{2} + b (12) + c$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$8 = a \cdot 8^{2} + b (8) + c$

$5 = a \cdot 12^{2} + b (12) + c$

Replace all occurrences of $c$ in $8 = a \cdot 8^{2} + b (8) + c$ with $15 - 4 a - 2 b$ .

$8 = a \cdot 8^{2} + b (8) + 15 - 4 a - 2 b$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$5 = a \cdot 12^{2} + b (12) + c$

Simplify $8 = a \cdot 8^{2} + b (8) + 15 - 4 a - 2 b$ .

Simplify the left side.

Remove parentheses.

$8 = a \cdot 8^{2} + b (8) + 15 - 4 a - 2 b$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$5 = a \cdot 12^{2} + b (12) + c$

$8 = a \cdot 8^{2} + b (8) + 15 - 4 a - 2 b$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$5 = a \cdot 12^{2} + b (12) + c$

Simplify the right side.

Simplify $a \cdot 8^{2} + b (8) + 15 - 4 a - 2 b$ .

Simplify each term.

Raise $8$ to the power of $2$ .

$8 = a \cdot 64 + b (8) + 15 - 4 a - 2 b$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$5 = a \cdot 12^{2} + b (12) + c$

Move $64$ to the left of $a$ .

$8 = 64 \cdot a + b (8) + 15 - 4 a - 2 b$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$5 = a \cdot 12^{2} + b (12) + c$

Move $8$ to the left of $b$ .

$8 = 64 a + 8 b + 15 - 4 a - 2 b$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$5 = a \cdot 12^{2} + b (12) + c$

$8 = 64 a + 8 b + 15 - 4 a - 2 b$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$5 = a \cdot 12^{2} + b (12) + c$

Simplify by adding terms.

Subtract $4 a$ from $64 a$ .

$8 = 60 a + 8 b + 15 - 2 b$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$5 = a \cdot 12^{2} + b (12) + c$

Subtract $2 b$ from $8 b$ .

$8 = 60 a + 6 b + 15$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$5 = a \cdot 12^{2} + b (12) + c$

$8 = 60 a + 6 b + 15$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$5 = a \cdot 12^{2} + b (12) + c$

$8 = 60 a + 6 b + 15$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$5 = a \cdot 12^{2} + b (12) + c$

$8 = 60 a + 6 b + 15$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$5 = a \cdot 12^{2} + b (12) + c$

$8 = 60 a + 6 b + 15$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$5 = a \cdot 12^{2} + b (12) + c$

Replace all occurrences of $c$ in $5 = a \cdot 12^{2} + b (12) + c$ with $15 - 4 a - 2 b$ .

$5 = a \cdot 12^{2} + b (12) + 15 - 4 a - 2 b$

$8 = 60 a + 6 b + 15$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Simplify $5 = a \cdot 12^{2} + b (12) + 15 - 4 a - 2 b$ .

Simplify the left side.

Remove parentheses.

$5 = a \cdot 12^{2} + b (12) + 15 - 4 a - 2 b$

$8 = 60 a + 6 b + 15$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$5 = a \cdot 12^{2} + b (12) + 15 - 4 a - 2 b$

$8 = 60 a + 6 b + 15$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Simplify the right side.

Simplify $a \cdot 12^{2} + b (12) + 15 - 4 a - 2 b$ .

Simplify each term.

Raise $12$ to the power of $2$ .

$5 = a \cdot 144 + b (12) + 15 - 4 a - 2 b$

$8 = 60 a + 6 b + 15$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Move $144$ to the left of $a$ .

$5 = 144 \cdot a + b (12) + 15 - 4 a - 2 b$

$8 = 60 a + 6 b + 15$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Move $12$ to the left of $b$ .

$5 = 144 a + 12 b + 15 - 4 a - 2 b$

$8 = 60 a + 6 b + 15$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$5 = 144 a + 12 b + 15 - 4 a - 2 b$

$8 = 60 a + 6 b + 15$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Simplify by adding terms.

Subtract $4 a$ from $144 a$ .

$5 = 140 a + 12 b + 15 - 2 b$

$8 = 60 a + 6 b + 15$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Subtract $2 b$ from $12 b$ .

$5 = 140 a + 10 b + 15$

$8 = 60 a + 6 b + 15$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$5 = 140 a + 10 b + 15$

$8 = 60 a + 6 b + 15$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$5 = 140 a + 10 b + 15$

$8 = 60 a + 6 b + 15$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$5 = 140 a + 10 b + 15$

$8 = 60 a + 6 b + 15$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$5 = 140 a + 10 b + 15$

$8 = 60 a + 6 b + 15$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$5 = 140 a + 10 b + 15$

$8 = 60 a + 6 b + 15$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Solve for $a$ in $5 = 140 a + 10 b + 15$ .

Rewrite the equation as $140 a + 10 b + 15 = 5$ .

$140 a + 10 b + 15 = 5$

$8 = 60 a + 6 b + 15$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Move all terms not containing $a$ to the right side of the equation.

Subtract $10 b$ from both sides of the equation.

$140 a + 15 = 5 - 10 b$

$8 = 60 a + 6 b + 15$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Subtract $15$ from both sides of the equation.

$140 a = 5 - 10 b - 15$

$8 = 60 a + 6 b + 15$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Subtract $15$ from $5$ .

$140 a = - 10 b - 10$

$8 = 60 a + 6 b + 15$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$140 a = - 10 b - 10$

$8 = 60 a + 6 b + 15$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Divide each term in $140 a = - 10 b - 10$ by $140$ and simplify.

Divide each term in $140 a = - 10 b - 10$ by $140$ .

$\frac{140 a}{140} = \frac{- 10 b}{140} + \frac{- 10}{140}$

$8 = 60 a + 6 b + 15$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Simplify the left side.

Cancel the common factor of $140$ .

Cancel the common factor.

$\frac{140 a}{140} = \frac{- 10 b}{140} + \frac{- 10}{140}$

$8 = 60 a + 6 b + 15$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Divide $a$ by $1$ .

$a = \frac{- 10 b}{140} + \frac{- 10}{140}$

$8 = 60 a + 6 b + 15$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$a = \frac{- 10 b}{140} + \frac{- 10}{140}$

$8 = 60 a + 6 b + 15$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$a = \frac{- 10 b}{140} + \frac{- 10}{140}$

$8 = 60 a + 6 b + 15$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Simplify the right side.

Simplify each term.

Cancel the common factor of $- 10$ and $140$ .

Factor $10$ out of $- 10 b$ .

$a = \frac{10 (- b)}{140} + \frac{- 10}{140}$

$8 = 60 a + 6 b + 15$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Cancel the common factors.

Factor $10$ out of $140$ .

$a = \frac{10 (- b)}{10 (14)} + \frac{- 10}{140}$

$8 = 60 a + 6 b + 15$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Cancel the common factor.

$a = \frac{10 (- b)}{10 \cdot 14} + \frac{- 10}{140}$

$8 = 60 a + 6 b + 15$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Rewrite the expression.

$a = \frac{- b}{14} + \frac{- 10}{140}$

$8 = 60 a + 6 b + 15$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$a = \frac{- b}{14} + \frac{- 10}{140}$

$8 = 60 a + 6 b + 15$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$a = \frac{- b}{14} + \frac{- 10}{140}$

$8 = 60 a + 6 b + 15$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Move the negative in front of the fraction.

$a = - \frac{b}{14} + \frac{- 10}{140}$

$8 = 60 a + 6 b + 15$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Cancel the common factor of $- 10$ and $140$ .

Factor $10$ out of $- 10$ .

$a = - \frac{b}{14} + \frac{10 (- 1)}{140}$

$8 = 60 a + 6 b + 15$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Cancel the common factors.

Factor $10$ out of $140$ .

$a = - \frac{b}{14} + \frac{10 \cdot - 1}{10 \cdot 14}$

$8 = 60 a + 6 b + 15$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Cancel the common factor.

$a = - \frac{b}{14} + \frac{10 \cdot - 1}{10 \cdot 14}$

$8 = 60 a + 6 b + 15$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Rewrite the expression.

$a = - \frac{b}{14} + \frac{- 1}{14}$

$8 = 60 a + 6 b + 15$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$a = - \frac{b}{14} + \frac{- 1}{14}$

$8 = 60 a + 6 b + 15$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$a = - \frac{b}{14} + \frac{- 1}{14}$

$8 = 60 a + 6 b + 15$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Move the negative in front of the fraction.

$a = - \frac{b}{14} - \frac{1}{14}$

$8 = 60 a + 6 b + 15$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$a = - \frac{b}{14} - \frac{1}{14}$

$8 = 60 a + 6 b + 15$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$a = - \frac{b}{14} - \frac{1}{14}$

$8 = 60 a + 6 b + 15$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$a = - \frac{b}{14} - \frac{1}{14}$

$8 = 60 a + 6 b + 15$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$a = - \frac{b}{14} - \frac{1}{14}$

$8 = 60 a + 6 b + 15$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Replace all occurrences of $a$ with $- \frac{b}{14} - \frac{1}{14}$ in each equation.

Replace all occurrences of $a$ in $8 = 60 a + 6 b + 15$ with $- \frac{b}{14} - \frac{1}{14}$ .

$8 = 60 (- \frac{b}{14} - \frac{1}{14}) + 6 b + 15$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Simplify the right side.

Simplify $60 (- \frac{b}{14} - \frac{1}{14}) + 6 b + 15$ .

Simplify each term.

Apply the distributive property.

$8 = 60 (- \frac{b}{14}) + 60 (- \frac{1}{14}) + 6 b + 15$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{b}{14}$ into the numerator.

$8 = 60 (\frac{- b}{14}) + 60 (- \frac{1}{14}) + 6 b + 15$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Factor $2$ out of $60$ .

$8 = 2 (30) (\frac{- b}{14}) + 60 (- \frac{1}{14}) + 6 b + 15$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Factor $2$ out of $14$ .

$8 = 2 \cdot (30 (\frac{- b}{2 \cdot 7})) + 60 (- \frac{1}{14}) + 6 b + 15$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Cancel the common factor.

$8 = 2 \cdot (30 (\frac{- b}{2 \cdot 7})) + 60 (- \frac{1}{14}) + 6 b + 15$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Rewrite the expression.

$8 = 30 (\frac{- b}{7}) + 60 (- \frac{1}{14}) + 6 b + 15$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$8 = 30 (\frac{- b}{7}) + 60 (- \frac{1}{14}) + 6 b + 15$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Combine $30$ and $\frac{- b}{7}$ .

$8 = \frac{30 (- b)}{7} + 60 (- \frac{1}{14}) + 6 b + 15$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Multiply $- 1$ by $30$ .

$8 = \frac{- 30 b}{7} + 60 (- \frac{1}{14}) + 6 b + 15$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{14}$ into the numerator.

$8 = \frac{- 30 b}{7} + 60 (\frac{- 1}{14}) + 6 b + 15$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Factor $2$ out of $60$ .

$8 = \frac{- 30 b}{7} + 2 (30) (\frac{- 1}{14}) + 6 b + 15$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Factor $2$ out of $14$ .

$8 = \frac{- 30 b}{7} + 2 \cdot (30 (\frac{- 1}{2 \cdot 7})) + 6 b + 15$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Cancel the common factor.

$8 = \frac{- 30 b}{7} + 2 \cdot (30 (\frac{- 1}{2 \cdot 7})) + 6 b + 15$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Rewrite the expression.

$8 = \frac{- 30 b}{7} + 30 (\frac{- 1}{7}) + 6 b + 15$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$8 = \frac{- 30 b}{7} + 30 (\frac{- 1}{7}) + 6 b + 15$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Combine $30$ and $\frac{- 1}{7}$ .

$8 = \frac{- 30 b}{7} + \frac{30 \cdot - 1}{7} + 6 b + 15$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Multiply $30$ by $- 1$ .

$8 = \frac{- 30 b}{7} + \frac{- 30}{7} + 6 b + 15$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Simplify each term.

Move the negative in front of the fraction.

$8 = - \frac{(30) b}{7} + \frac{- 30}{7} + 6 b + 15$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Move the negative in front of the fraction.

$8 = - \frac{30 b}{7} - \frac{30}{7} + 6 b + 15$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$8 = - \frac{30 b}{7} - \frac{30}{7} + 6 b + 15$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$8 = - \frac{30 b}{7} - \frac{30}{7} + 6 b + 15$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

To write $6 b$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$8 = - \frac{30 b}{7} + 6 b \cdot \frac{7}{7} - \frac{30}{7} + 15$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Combine $6 b$ and $\frac{7}{7}$ .

$8 = - \frac{30 b}{7} + \frac{6 b \cdot 7}{7} - \frac{30}{7} + 15$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Combine the numerators over the common denominator.

$8 = \frac{- 30 b + 6 b \cdot 7}{7} - \frac{30}{7} + 15$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Combine the numerators over the common denominator.

$8 = 15 + \frac{- 30 b + 6 b \cdot 7 - 30}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Multiply $7$ by $6$ .

$8 = 15 + \frac{- 30 b + 42 b - 30}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Add $- 30 b$ and $42 b$ .

$8 = 15 + \frac{12 b - 30}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Factor $6$ out of $12 b - 30$ .

Factor $6$ out of $12 b$ .

$8 = 15 + \frac{6 (2 b) - 30}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Factor $6$ out of $- 30$ .

$8 = 15 + \frac{6 (2 b) + 6 (- 5)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Factor $6$ out of $6 (2 b) + 6 (- 5)$ .

$8 = 15 + \frac{6 (2 b - 5)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$8 = 15 + \frac{6 (2 b - 5)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

To write $15$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$8 = 15 \cdot \frac{7}{7} + \frac{6 (2 b - 5)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Simplify terms.

Combine $15$ and $\frac{7}{7}$ .

$8 = \frac{15 \cdot 7}{7} + \frac{6 (2 b - 5)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Combine the numerators over the common denominator.

$8 = \frac{15 \cdot 7 + 6 (2 b - 5)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$8 = \frac{15 \cdot 7 + 6 (2 b - 5)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Simplify the numerator.

Factor $3$ out of $15 \cdot 7 + 6 (2 b - 5)$ .

Factor $3$ out of $15 \cdot 7$ .

$8 = \frac{3 (5 \cdot 7) + 6 (2 b - 5)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Factor $3$ out of $6 (2 b - 5)$ .

$8 = \frac{3 (5 \cdot 7) + 3 (2 (2 b - 5))}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Factor $3$ out of $3 (5 \cdot 7) + 3 (2 (2 b - 5))$ .

$8 = \frac{3 (5 \cdot 7 + 2 (2 b - 5))}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$8 = \frac{3 (5 \cdot 7 + 2 (2 b - 5))}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Multiply $5$ by $7$ .

$8 = \frac{3 (35 + 2 (2 b - 5))}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Apply the distributive property.

$8 = \frac{3 (35 + 2 (2 b) + 2 \cdot - 5)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Multiply $2$ by $2$ .

$8 = \frac{3 (35 + 4 b + 2 \cdot - 5)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Multiply $2$ by $- 5$ .

$8 = \frac{3 (35 + 4 b - 10)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Subtract $10$ from $35$ .

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = 45 a + 5 b + 15$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Replace all occurrences of $a$ in $9 = 45 a + 5 b + 15$ with $- \frac{b}{14} - \frac{1}{14}$ .

$9 = 45 (- \frac{b}{14} - \frac{1}{14}) + 5 b + 15$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Simplify the right side.

Simplify $45 (- \frac{b}{14} - \frac{1}{14}) + 5 b + 15$ .

Simplify each term.

Apply the distributive property.

$9 = 45 (- \frac{b}{14}) + 45 (- \frac{1}{14}) + 5 b + 15$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Multiply $45 (- \frac{b}{14})$ .

Multiply $- 1$ by $45$ .

$9 = - 45 \frac{b}{14} + 45 (- \frac{1}{14}) + 5 b + 15$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Combine $- 45$ and $\frac{b}{14}$ .

$9 = \frac{- 45 b}{14} + 45 (- \frac{1}{14}) + 5 b + 15$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$9 = \frac{- 45 b}{14} + 45 (- \frac{1}{14}) + 5 b + 15$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Multiply $45 (- \frac{1}{14})$ .

Multiply $- 1$ by $45$ .

$9 = \frac{- 45 b}{14} - 45 (\frac{1}{14}) + 5 b + 15$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Combine $- 45$ and $\frac{1}{14}$ .

$9 = \frac{- 45 b}{14} + \frac{- 45}{14} + 5 b + 15$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$9 = \frac{- 45 b}{14} + \frac{- 45}{14} + 5 b + 15$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Simplify each term.

Move the negative in front of the fraction.

$9 = - \frac{(45) b}{14} + \frac{- 45}{14} + 5 b + 15$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Move the negative in front of the fraction.

$9 = - \frac{45 b}{14} - \frac{45}{14} + 5 b + 15$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$9 = - \frac{45 b}{14} - \frac{45}{14} + 5 b + 15$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$9 = - \frac{45 b}{14} - \frac{45}{14} + 5 b + 15$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

To write $5 b$ as a fraction with a common denominator, multiply by $\frac{14}{14}$ .

$9 = - \frac{45 b}{14} + 5 b \cdot \frac{14}{14} - \frac{45}{14} + 15$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Combine $5 b$ and $\frac{14}{14}$ .

$9 = - \frac{45 b}{14} + \frac{5 b \cdot 14}{14} - \frac{45}{14} + 15$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Combine the numerators over the common denominator.

$9 = \frac{- 45 b + 5 b \cdot 14}{14} - \frac{45}{14} + 15$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Combine the numerators over the common denominator.

$9 = 15 + \frac{- 45 b + 5 b \cdot 14 - 45}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Multiply $14$ by $5$ .

$9 = 15 + \frac{- 45 b + 70 b - 45}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Add $- 45 b$ and $70 b$ .

$9 = 15 + \frac{25 b - 45}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Factor $5$ out of $25 b - 45$ .

Factor $5$ out of $25 b$ .

$9 = 15 + \frac{5 (5 b) - 45}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Factor $5$ out of $- 45$ .

$9 = 15 + \frac{5 (5 b) + 5 (- 9)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Factor $5$ out of $5 (5 b) + 5 (- 9)$ .

$9 = 15 + \frac{5 (5 b - 9)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$9 = 15 + \frac{5 (5 b - 9)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

To write $15$ as a fraction with a common denominator, multiply by $\frac{14}{14}$ .

$9 = 15 \cdot \frac{14}{14} + \frac{5 (5 b - 9)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Simplify terms.

Combine $15$ and $\frac{14}{14}$ .

$9 = \frac{15 \cdot 14}{14} + \frac{5 (5 b - 9)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Combine the numerators over the common denominator.

$9 = \frac{15 \cdot 14 + 5 (5 b - 9)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$9 = \frac{15 \cdot 14 + 5 (5 b - 9)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Simplify the numerator.

Factor $5$ out of $15 \cdot 14 + 5 (5 b - 9)$ .

Factor $5$ out of $15 \cdot 14$ .

$9 = \frac{5 (3 \cdot 14) + 5 (5 b - 9)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Factor $5$ out of $5 (3 \cdot 14) + 5 (5 b - 9)$ .

$9 = \frac{5 (3 \cdot 14 + 5 b - 9)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$9 = \frac{5 (3 \cdot 14 + 5 b - 9)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Multiply $3$ by $14$ .

$9 = \frac{5 (42 + 5 b - 9)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Subtract $9$ from $42$ .

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$13 = 32 a + 4 b + 15$

$c = 15 - 4 a - 2 b$

Replace all occurrences of $a$ in $13 = 32 a + 4 b + 15$ with $- \frac{b}{14} - \frac{1}{14}$ .

$13 = 32 (- \frac{b}{14} - \frac{1}{14}) + 4 b + 15$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15 - 4 a - 2 b$

Simplify the right side.

Simplify $32 (- \frac{b}{14} - \frac{1}{14}) + 4 b + 15$ .

Simplify each term.

Apply the distributive property.

$13 = 32 (- \frac{b}{14}) + 32 (- \frac{1}{14}) + 4 b + 15$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15 - 4 a - 2 b$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{b}{14}$ into the numerator.

$13 = 32 (\frac{- b}{14}) + 32 (- \frac{1}{14}) + 4 b + 15$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15 - 4 a - 2 b$

Factor $2$ out of $32$ .

$13 = 2 (16) (\frac{- b}{14}) + 32 (- \frac{1}{14}) + 4 b + 15$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15 - 4 a - 2 b$

Factor $2$ out of $14$ .

$13 = 2 \cdot (16 (\frac{- b}{2 \cdot 7})) + 32 (- \frac{1}{14}) + 4 b + 15$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15 - 4 a - 2 b$

Cancel the common factor.

$13 = 2 \cdot (16 (\frac{- b}{2 \cdot 7})) + 32 (- \frac{1}{14}) + 4 b + 15$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15 - 4 a - 2 b$

Rewrite the expression.

$13 = 16 (\frac{- b}{7}) + 32 (- \frac{1}{14}) + 4 b + 15$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15 - 4 a - 2 b$

$13 = 16 (\frac{- b}{7}) + 32 (- \frac{1}{14}) + 4 b + 15$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15 - 4 a - 2 b$

Combine $16$ and $\frac{- b}{7}$ .

$13 = \frac{16 (- b)}{7} + 32 (- \frac{1}{14}) + 4 b + 15$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15 - 4 a - 2 b$

Multiply $- 1$ by $16$ .

$13 = \frac{- 16 b}{7} + 32 (- \frac{1}{14}) + 4 b + 15$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15 - 4 a - 2 b$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{14}$ into the numerator.

$13 = \frac{- 16 b}{7} + 32 (\frac{- 1}{14}) + 4 b + 15$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15 - 4 a - 2 b$

Factor $2$ out of $32$ .

$13 = \frac{- 16 b}{7} + 2 (16) (\frac{- 1}{14}) + 4 b + 15$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15 - 4 a - 2 b$

Factor $2$ out of $14$ .

$13 = \frac{- 16 b}{7} + 2 \cdot (16 (\frac{- 1}{2 \cdot 7})) + 4 b + 15$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15 - 4 a - 2 b$

Cancel the common factor.

$13 = \frac{- 16 b}{7} + 2 \cdot (16 (\frac{- 1}{2 \cdot 7})) + 4 b + 15$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15 - 4 a - 2 b$

Rewrite the expression.

$13 = \frac{- 16 b}{7} + 16 (\frac{- 1}{7}) + 4 b + 15$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15 - 4 a - 2 b$

$13 = \frac{- 16 b}{7} + 16 (\frac{- 1}{7}) + 4 b + 15$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15 - 4 a - 2 b$

Combine $16$ and $\frac{- 1}{7}$ .

$13 = \frac{- 16 b}{7} + \frac{16 \cdot - 1}{7} + 4 b + 15$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15 - 4 a - 2 b$

Multiply $16$ by $- 1$ .

$13 = \frac{- 16 b}{7} + \frac{- 16}{7} + 4 b + 15$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15 - 4 a - 2 b$

Simplify each term.

Move the negative in front of the fraction.

$13 = - \frac{(16) b}{7} + \frac{- 16}{7} + 4 b + 15$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15 - 4 a - 2 b$

Move the negative in front of the fraction.

$13 = - \frac{16 b}{7} - \frac{16}{7} + 4 b + 15$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15 - 4 a - 2 b$

$13 = - \frac{16 b}{7} - \frac{16}{7} + 4 b + 15$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15 - 4 a - 2 b$

$13 = - \frac{16 b}{7} - \frac{16}{7} + 4 b + 15$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15 - 4 a - 2 b$

To write $4 b$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$13 = - \frac{16 b}{7} + 4 b \cdot \frac{7}{7} - \frac{16}{7} + 15$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15 - 4 a - 2 b$

Combine $4 b$ and $\frac{7}{7}$ .

$13 = - \frac{16 b}{7} + \frac{4 b \cdot 7}{7} - \frac{16}{7} + 15$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15 - 4 a - 2 b$

Combine the numerators over the common denominator.

$13 = \frac{- 16 b + 4 b \cdot 7}{7} - \frac{16}{7} + 15$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15 - 4 a - 2 b$

Combine the numerators over the common denominator.

$13 = 15 + \frac{- 16 b + 4 b \cdot 7 - 16}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15 - 4 a - 2 b$

Multiply $7$ by $4$ .

$13 = 15 + \frac{- 16 b + 28 b - 16}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15 - 4 a - 2 b$

Add $- 16 b$ and $28 b$ .

$13 = 15 + \frac{12 b - 16}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15 - 4 a - 2 b$

Factor $4$ out of $12 b - 16$ .

Factor $4$ out of $12 b$ .

$13 = 15 + \frac{4 (3 b) - 16}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15 - 4 a - 2 b$

Factor $4$ out of $- 16$ .

$13 = 15 + \frac{4 (3 b) + 4 (- 4)}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15 - 4 a - 2 b$

Factor $4$ out of $4 (3 b) + 4 (- 4)$ .

$13 = 15 + \frac{4 (3 b - 4)}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15 - 4 a - 2 b$

$13 = 15 + \frac{4 (3 b - 4)}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15 - 4 a - 2 b$

To write $15$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$13 = 15 \cdot \frac{7}{7} + \frac{4 (3 b - 4)}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15 - 4 a - 2 b$

Simplify terms.

Combine $15$ and $\frac{7}{7}$ .

$13 = \frac{15 \cdot 7}{7} + \frac{4 (3 b - 4)}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15 - 4 a - 2 b$

Combine the numerators over the common denominator.

$13 = \frac{15 \cdot 7 + 4 (3 b - 4)}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15 - 4 a - 2 b$

$13 = \frac{15 \cdot 7 + 4 (3 b - 4)}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15 - 4 a - 2 b$

Simplify the numerator.

Multiply $15$ by $7$ .

$13 = \frac{105 + 4 (3 b - 4)}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15 - 4 a - 2 b$

Apply the distributive property.

$13 = \frac{105 + 4 (3 b) + 4 \cdot - 4}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15 - 4 a - 2 b$

Multiply $3$ by $4$ .

$13 = \frac{105 + 12 b + 4 \cdot - 4}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15 - 4 a - 2 b$

Multiply $4$ by $- 4$ .

$13 = \frac{105 + 12 b - 16}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15 - 4 a - 2 b$

Subtract $16$ from $105$ .

$13 = \frac{12 b + 89}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15 - 4 a - 2 b$

$13 = \frac{12 b + 89}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15 - 4 a - 2 b$

$13 = \frac{12 b + 89}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15 - 4 a - 2 b$

$13 = \frac{12 b + 89}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15 - 4 a - 2 b$

Replace all occurrences of $a$ in $c = 15 - 4 a - 2 b$ with $- \frac{b}{14} - \frac{1}{14}$ .

$c = 15 - 4 (- \frac{b}{14} - \frac{1}{14}) - 2 b$

$13 = \frac{12 b + 89}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Simplify the right side.

Simplify $15 - 4 (- \frac{b}{14} - \frac{1}{14}) - 2 b$ .

Simplify each term.

Apply the distributive property.

$c = 15 - 4 (- \frac{b}{14}) - 4 (- \frac{1}{14}) - 2 b$

$13 = \frac{12 b + 89}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{b}{14}$ into the numerator.

$c = 15 - 4 \frac{- b}{14} - 4 (- \frac{1}{14}) - 2 b$

$13 = \frac{12 b + 89}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Factor $2$ out of $- 4$ .

$c = 15 + 2 (- 2) (\frac{- b}{14}) - 4 (- \frac{1}{14}) - 2 b$

$13 = \frac{12 b + 89}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Factor $2$ out of $14$ .

$c = 15 + 2 \cdot (- 2 \frac{- b}{2 \cdot 7}) - 4 (- \frac{1}{14}) - 2 b$

$13 = \frac{12 b + 89}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Cancel the common factor.

$c = 15 + 2 \cdot (- 2 \frac{- b}{2 \cdot 7}) - 4 (- \frac{1}{14}) - 2 b$

$13 = \frac{12 b + 89}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Rewrite the expression.

$c = 15 - 2 \frac{- b}{7} - 4 (- \frac{1}{14}) - 2 b$

$13 = \frac{12 b + 89}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15 - 2 \frac{- b}{7} - 4 (- \frac{1}{14}) - 2 b$

$13 = \frac{12 b + 89}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Combine $- 2$ and $\frac{- b}{7}$ .

$c = 15 + \frac{- 2 (- b)}{7} - 4 (- \frac{1}{14}) - 2 b$

$13 = \frac{12 b + 89}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Multiply $- 1$ by $- 2$ .

$c = 15 + \frac{2 b}{7} - 4 (- \frac{1}{14}) - 2 b$

$13 = \frac{12 b + 89}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{14}$ into the numerator.

$c = 15 + \frac{2 b}{7} - 4 (\frac{- 1}{14}) - 2 b$

$13 = \frac{12 b + 89}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Factor $2$ out of $- 4$ .

$c = 15 + \frac{2 b}{7} + 2 (- 2) (\frac{- 1}{14}) - 2 b$

$13 = \frac{12 b + 89}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Factor $2$ out of $14$ .

$c = 15 + \frac{2 b}{7} + 2 \cdot (- 2 \frac{- 1}{2 \cdot 7}) - 2 b$

$13 = \frac{12 b + 89}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Cancel the common factor.

$c = 15 + \frac{2 b}{7} + 2 \cdot (- 2 \frac{- 1}{2 \cdot 7}) - 2 b$

$13 = \frac{12 b + 89}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Rewrite the expression.

$c = 15 + \frac{2 b}{7} - 2 (\frac{- 1}{7}) - 2 b$

$13 = \frac{12 b + 89}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15 + \frac{2 b}{7} - 2 (\frac{- 1}{7}) - 2 b$

$13 = \frac{12 b + 89}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Combine $- 2$ and $\frac{- 1}{7}$ .

$c = 15 + \frac{2 b}{7} + \frac{- 2 \cdot - 1}{7} - 2 b$

$13 = \frac{12 b + 89}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Multiply $- 2$ by $- 1$ .

$c = 15 + \frac{2 b}{7} + \frac{2}{7} - 2 b$

$13 = \frac{12 b + 89}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15 + \frac{2 b}{7} + \frac{2}{7} - 2 b$

$13 = \frac{12 b + 89}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

To write $15$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$c = \frac{2 b}{7} + 15 \cdot \frac{7}{7} + \frac{2}{7} - 2 b$

$13 = \frac{12 b + 89}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Combine $15$ and $\frac{7}{7}$ .

$c = \frac{2 b}{7} + \frac{15 \cdot 7}{7} + \frac{2}{7} - 2 b$

$13 = \frac{12 b + 89}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Combine the numerators over the common denominator.

$c = \frac{2 b}{7} + \frac{15 \cdot 7 + 2}{7} - 2 b$

$13 = \frac{12 b + 89}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Simplify the numerator.

Multiply $15$ by $7$ .

$c = \frac{2 b}{7} + \frac{105 + 2}{7} - 2 b$

$13 = \frac{12 b + 89}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Add $105$ and $2$ .

$c = \frac{2 b}{7} + \frac{107}{7} - 2 b$

$13 = \frac{12 b + 89}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = \frac{2 b}{7} + \frac{107}{7} - 2 b$

$13 = \frac{12 b + 89}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

To write $- 2 b$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$c = \frac{2 b}{7} - 2 b \cdot \frac{7}{7} + \frac{107}{7}$

$13 = \frac{12 b + 89}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Combine $- 2 b$ and $\frac{7}{7}$ .

$c = \frac{2 b}{7} + \frac{- 2 b \cdot 7}{7} + \frac{107}{7}$

$13 = \frac{12 b + 89}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Combine the numerators over the common denominator.

$c = \frac{2 b - 2 b \cdot 7}{7} + \frac{107}{7}$

$13 = \frac{12 b + 89}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Combine the numerators over the common denominator.

$c = \frac{2 b - 2 b \cdot 7 + 107}{7}$

$13 = \frac{12 b + 89}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Multiply $7$ by $- 2$ .

$c = \frac{2 b - 14 b + 107}{7}$

$13 = \frac{12 b + 89}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Subtract $14 b$ from $2 b$ .

$c = \frac{- 12 b + 107}{7}$

$13 = \frac{12 b + 89}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Factor $- 1$ out of $- 12 b$ .

$c = \frac{- (12 b) + 107}{7}$

$13 = \frac{12 b + 89}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Rewrite $107$ as $- 1 (- 107)$ .

$c = \frac{- (12 b) - 1 \cdot - 107}{7}$

$13 = \frac{12 b + 89}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Factor $- 1$ out of $- (12 b) - 1 (- 107)$ .

$c = \frac{- (12 b - 107)}{7}$

$13 = \frac{12 b + 89}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Simplify the expression.

Rewrite $- (12 b - 107)$ as $- 1 (12 b - 107)$ .

$c = \frac{- 1 (12 b - 107)}{7}$

$13 = \frac{12 b + 89}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Move the negative in front of the fraction.

$c = - \frac{12 b - 107}{7}$

$13 = \frac{12 b + 89}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = - \frac{12 b - 107}{7}$

$13 = \frac{12 b + 89}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = - \frac{12 b - 107}{7}$

$13 = \frac{12 b + 89}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = - \frac{12 b - 107}{7}$

$13 = \frac{12 b + 89}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = - \frac{12 b - 107}{7}$

$13 = \frac{12 b + 89}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Solve for $b$ in $13 = \frac{12 b + 89}{7}$ .

Rewrite the equation as $\frac{12 b + 89}{7} = 13$ .

$\frac{12 b + 89}{7} = 13$

$c = - \frac{12 b - 107}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Multiply both sides by $7$ .

$\frac{12 b + 89}{7} \cdot 7 = 13 \cdot 7$

$c = - \frac{12 b - 107}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Simplify.

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{12 b + 89}{7} \cdot 7 = 13 \cdot 7$

$c = - \frac{12 b - 107}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Rewrite the expression.

$12 b + 89 = 13 \cdot 7$

$c = - \frac{12 b - 107}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$12 b + 89 = 13 \cdot 7$

$c = - \frac{12 b - 107}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$12 b + 89 = 13 \cdot 7$

$c = - \frac{12 b - 107}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Simplify the right side.

Multiply $13$ by $7$ .

$12 b + 89 = 91$

$c = - \frac{12 b - 107}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$12 b + 89 = 91$

$c = - \frac{12 b - 107}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$12 b + 89 = 91$

$c = - \frac{12 b - 107}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Solve for $b$ .

Move all terms not containing $b$ to the right side of the equation.

Subtract $89$ from both sides of the equation.

$12 b = 91 - 89$

$c = - \frac{12 b - 107}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Subtract $89$ from $91$ .

$12 b = 2$

$c = - \frac{12 b - 107}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$12 b = 2$

$c = - \frac{12 b - 107}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Divide each term in $12 b = 2$ by $12$ and simplify.

Divide each term in $12 b = 2$ by $12$ .

$\frac{12 b}{12} = \frac{2}{12}$

$c = - \frac{12 b - 107}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Simplify the left side.

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{12 b}{12} = \frac{2}{12}$

$c = - \frac{12 b - 107}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Divide $b$ by $1$ .

$b = \frac{2}{12}$

$c = - \frac{12 b - 107}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$b = \frac{2}{12}$

$c = - \frac{12 b - 107}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$b = \frac{2}{12}$

$c = - \frac{12 b - 107}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Simplify the right side.

Cancel the common factor of $2$ and $12$ .

Factor $2$ out of $2$ .

$b = \frac{2 (1)}{12}$

$c = - \frac{12 b - 107}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Cancel the common factors.

Factor $2$ out of $12$ .

$b = \frac{2 \cdot 1}{2 \cdot 6}$

$c = - \frac{12 b - 107}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Cancel the common factor.

$b = \frac{2 \cdot 1}{2 \cdot 6}$

$c = - \frac{12 b - 107}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Rewrite the expression.

$b = \frac{1}{6}$

$c = - \frac{12 b - 107}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$b = \frac{1}{6}$

$c = - \frac{12 b - 107}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$b = \frac{1}{6}$

$c = - \frac{12 b - 107}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$b = \frac{1}{6}$

$c = - \frac{12 b - 107}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$b = \frac{1}{6}$

$c = - \frac{12 b - 107}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$b = \frac{1}{6}$

$c = - \frac{12 b - 107}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$b = \frac{1}{6}$

$c = - \frac{12 b - 107}{7}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Replace all occurrences of $b$ with $\frac{1}{6}$ in each equation.

Replace all occurrences of $b$ in $c = - \frac{12 b - 107}{7}$ with $\frac{1}{6}$ .

$c = - \frac{12 (\frac{1}{6}) - 107}{7}$

$b = \frac{1}{6}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Simplify the right side.

Simplify $- \frac{12 (\frac{1}{6}) - 107}{7}$ .

Simplify the numerator.

Cancel the common factor of $6$ .

Factor $6$ out of $12$ .

$c = - \frac{6 (2) (\frac{1}{6}) - 107}{7}$

$b = \frac{1}{6}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Cancel the common factor.

$c = - \frac{6 \cdot (2 (\frac{1}{6})) - 107}{7}$

$b = \frac{1}{6}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Rewrite the expression.

$c = - \frac{2 - 107}{7}$

$b = \frac{1}{6}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = - \frac{2 - 107}{7}$

$b = \frac{1}{6}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Subtract $107$ from $2$ .

$c = - \frac{- 105}{7}$

$b = \frac{1}{6}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = - \frac{- 105}{7}$

$b = \frac{1}{6}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Simplify the expression.

Divide $- 105$ by $7$ .

$c = 15$

$b = \frac{1}{6}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Multiply $- 1$ by $- 15$ .

$c = 15$

$b = \frac{1}{6}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15$

$b = \frac{1}{6}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15$

$b = \frac{1}{6}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$c = 15$

$b = \frac{1}{6}$

$9 = \frac{5 (5 b + 33)}{14}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Replace all occurrences of $b$ in $9 = \frac{5 (5 b + 33)}{14}$ with $\frac{1}{6}$ .

$9 = \frac{5 (5 (\frac{1}{6}) + 33)}{14}$

$c = 15$

$b = \frac{1}{6}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Simplify the right side.

Simplify $\frac{5 (5 (\frac{1}{6}) + 33)}{14}$ .

Simplify the numerator.

Combine $5$ and $\frac{1}{6}$ .

$9 = \frac{5 (\frac{5}{6} + 33)}{14}$

$c = 15$

$b = \frac{1}{6}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

To write $33$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$9 = \frac{5 (\frac{5}{6} + 33 \cdot \frac{6}{6})}{14}$

$c = 15$

$b = \frac{1}{6}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Combine $33$ and $\frac{6}{6}$ .

$9 = \frac{5 (\frac{5}{6} + \frac{33 \cdot 6}{6})}{14}$

$c = 15$

$b = \frac{1}{6}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Combine the numerators over the common denominator.

$9 = \frac{5 (\frac{5 + 33 \cdot 6}{6})}{14}$

$c = 15$

$b = \frac{1}{6}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Simplify the numerator.

Multiply $33$ by $6$ .

$9 = \frac{5 (\frac{5 + 198}{6})}{14}$

$c = 15$

$b = \frac{1}{6}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Add $5$ and $198$ .

$9 = \frac{5 (\frac{203}{6})}{14}$

$c = 15$

$b = \frac{1}{6}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = \frac{5 (\frac{203}{6})}{14}$

$c = 15$

$b = \frac{1}{6}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = \frac{5 (\frac{203}{6})}{14}$

$c = 15$

$b = \frac{1}{6}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Combine fractions.

Combine $5$ and $\frac{203}{6}$ .

$9 = \frac{\frac{5 \cdot 203}{6}}{14}$

$c = 15$

$b = \frac{1}{6}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Multiply $5$ by $203$ .

$9 = \frac{\frac{1015}{6}}{14}$

$c = 15$

$b = \frac{1}{6}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = \frac{\frac{1015}{6}}{14}$

$c = 15$

$b = \frac{1}{6}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Multiply the numerator by the reciprocal of the denominator.

$9 = \frac{1015}{6} \cdot \frac{1}{14}$

$c = 15$

$b = \frac{1}{6}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Cancel the common factor of $7$ .

Factor $7$ out of $1015$ .

$9 = \frac{7 (145)}{6} \cdot \frac{1}{14}$

$c = 15$

$b = \frac{1}{6}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Factor $7$ out of $14$ .

$9 = \frac{7 \cdot 145}{6} \cdot \frac{1}{7 \cdot 2}$

$c = 15$

$b = \frac{1}{6}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Cancel the common factor.

$9 = \frac{7 \cdot 145}{6} \cdot \frac{1}{7 \cdot 2}$

$c = 15$

$b = \frac{1}{6}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Rewrite the expression.

$9 = \frac{145}{6} \cdot \frac{1}{2}$

$c = 15$

$b = \frac{1}{6}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = \frac{145}{6} \cdot \frac{1}{2}$

$c = 15$

$b = \frac{1}{6}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Multiply $\frac{145}{6}$ by $\frac{1}{2}$ .

$9 = \frac{145}{6 \cdot 2}$

$c = 15$

$b = \frac{1}{6}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Multiply $6$ by $2$ .

$9 = \frac{145}{12}$

$c = 15$

$b = \frac{1}{6}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = \frac{145}{12}$

$c = 15$

$b = \frac{1}{6}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

$9 = \frac{145}{12}$

$c = 15$

$b = \frac{1}{6}$

$8 = \frac{3 (4 b + 25)}{7}$

$a = - \frac{b}{14} - \frac{1}{14}$

Replace all occurrences of $b$ in $8 = \frac{3 (4 b + 25)}{7}$ with $\frac{1}{6}$ .

$8 = \frac{3 (4 (\frac{1}{6}) + 25)}{7}$

$9 = \frac{145}{12}$

$c = 15$

$b = \frac{1}{6}$

$a = - \frac{b}{14} - \frac{1}{14}$

Simplify the right side.

Simplify $\frac{3 (4 (\frac{1}{6}) + 25)}{7}$ .

Simplify the numerator.

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$8 = \frac{3 (2 (2) (\frac{1}{6}) + 25)}{7}$

$9 = \frac{145}{12}$

$c = 15$

$b = \frac{1}{6}$

$a = - \frac{b}{14} - \frac{1}{14}$

Factor $2$ out of $6$ .

$8 = \frac{3 (2 \cdot (2 (\frac{1}{2 \cdot 3})) + 25)}{7}$

$9 = \frac{145}{12}$

$c = 15$

$b = \frac{1}{6}$

$a = - \frac{b}{14} - \frac{1}{14}$

Cancel the common factor.

$8 = \frac{3 (2 \cdot (2 (\frac{1}{2 \cdot 3})) + 25)}{7}$

$9 = \frac{145}{12}$

$c = 15$

$b = \frac{1}{6}$

$a = - \frac{b}{14} - \frac{1}{14}$

Rewrite the expression.

$8 = \frac{3 (2 (\frac{1}{3}) + 25)}{7}$

$9 = \frac{145}{12}$

$c = 15$

$b = \frac{1}{6}$

$a = - \frac{b}{14} - \frac{1}{14}$

$8 = \frac{3 (2 (\frac{1}{3}) + 25)}{7}$

$9 = \frac{145}{12}$

$c = 15$

$b = \frac{1}{6}$

$a = - \frac{b}{14} - \frac{1}{14}$

Combine $2$ and $\frac{1}{3}$ .

$8 = \frac{3 (\frac{2}{3} + 25)}{7}$

$9 = \frac{145}{12}$

$c = 15$

$b = \frac{1}{6}$

$a = - \frac{b}{14} - \frac{1}{14}$

To write $25$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$8 = \frac{3 (\frac{2}{3} + 25 \cdot \frac{3}{3})}{7}$

$9 = \frac{145}{12}$

$c = 15$

$b = \frac{1}{6}$

$a = - \frac{b}{14} - \frac{1}{14}$

Combine $25$ and $\frac{3}{3}$ .

$8 = \frac{3 (\frac{2}{3} + \frac{25 \cdot 3}{3})}{7}$

$9 = \frac{145}{12}$

$c = 15$

$b = \frac{1}{6}$

$a = - \frac{b}{14} - \frac{1}{14}$

Combine the numerators over the common denominator.

$8 = \frac{3 (\frac{2 + 25 \cdot 3}{3})}{7}$

$9 = \frac{145}{12}$

$c = 15$

$b = \frac{1}{6}$

$a = - \frac{b}{14} - \frac{1}{14}$

Simplify the numerator.

Multiply $25$ by $3$ .

$8 = \frac{3 (\frac{2 + 75}{3})}{7}$

$9 = \frac{145}{12}$

$c = 15$

$b = \frac{1}{6}$

$a = - \frac{b}{14} - \frac{1}{14}$

Add $2$ and $75$ .

$8 = \frac{3 (\frac{77}{3})}{7}$

$9 = \frac{145}{12}$

$c = 15$

$b = \frac{1}{6}$

$a = - \frac{b}{14} - \frac{1}{14}$

$8 = \frac{3 (\frac{77}{3})}{7}$

$9 = \frac{145}{12}$

$c = 15$

$b = \frac{1}{6}$

$a = - \frac{b}{14} - \frac{1}{14}$

$8 = \frac{3 (\frac{77}{3})}{7}$

$9 = \frac{145}{12}$

$c = 15$

$b = \frac{1}{6}$

$a = - \frac{b}{14} - \frac{1}{14}$

Combine fractions.

Combine $3$ and $\frac{77}{3}$ .

$8 = \frac{\frac{3 \cdot 77}{3}}{7}$

$9 = \frac{145}{12}$

$c = 15$

$b = \frac{1}{6}$

$a = - \frac{b}{14} - \frac{1}{14}$

Simplify the expression.

Multiply $3$ by $77$ .

$8 = \frac{\frac{231}{3}}{7}$

$9 = \frac{145}{12}$

$c = 15$

$b = \frac{1}{6}$

$a = - \frac{b}{14} - \frac{1}{14}$

Divide $231$ by $3$ .

$8 = \frac{77}{7}$

$9 = \frac{145}{12}$

$c = 15$

$b = \frac{1}{6}$

$a = - \frac{b}{14} - \frac{1}{14}$

Divide $77$ by $7$ .

$8 = 11$

$9 = \frac{145}{12}$

$c = 15$

$b = \frac{1}{6}$

$a = - \frac{b}{14} - \frac{1}{14}$

$8 = 11$

$9 = \frac{145}{12}$

$c = 15$

$b = \frac{1}{6}$

$a = - \frac{b}{14} - \frac{1}{14}$

$8 = 11$

$9 = \frac{145}{12}$

$c = 15$

$b = \frac{1}{6}$

$a = - \frac{b}{14} - \frac{1}{14}$

$8 = 11$

$9 = \frac{145}{12}$

$c = 15$

$b = \frac{1}{6}$

$a = - \frac{b}{14} - \frac{1}{14}$

$8 = 11$

$9 = \frac{145}{12}$

$c = 15$

$b = \frac{1}{6}$

$a = - \frac{b}{14} - \frac{1}{14}$

Replace all occurrences of $b$ in $a = - \frac{b}{14} - \frac{1}{14}$ with $\frac{1}{6}$ .

$a = - \frac{\frac{1}{6}}{14} - \frac{1}{14}$

$8 = 11$

$9 = \frac{145}{12}$

$c = 15$

$b = \frac{1}{6}$

Simplify the right side.

Simplify $- \frac{\frac{1}{6}}{14} - \frac{1}{14}$ .

Combine the numerators over the common denominator.

$a = \frac{- \frac{1}{6} - 1}{14}$

$8 = 11$

$9 = \frac{145}{12}$

$c = 15$

$b = \frac{1}{6}$

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$a = \frac{- \frac{1}{6} - 1 \cdot \frac{6}{6}}{14}$

$8 = 11$

$9 = \frac{145}{12}$

$c = 15$

$b = \frac{1}{6}$

Combine $- 1$ and $\frac{6}{6}$ .

$a = \frac{- \frac{1}{6} + \frac{- 1 \cdot 6}{6}}{14}$

$8 = 11$

$9 = \frac{145}{12}$

$c = 15$

$b = \frac{1}{6}$

Combine the numerators over the common denominator.

$a = \frac{\frac{- 1 - 1 \cdot 6}{6}}{14}$

$8 = 11$

$9 = \frac{145}{12}$

$c = 15$

$b = \frac{1}{6}$

Simplify the numerator.

Multiply $- 1$ by $6$ .

$a = \frac{\frac{- 1 - 6}{6}}{14}$

$8 = 11$

$9 = \frac{145}{12}$

$c = 15$

$b = \frac{1}{6}$

Subtract $6$ from $- 1$ .

$a = \frac{\frac{- 7}{6}}{14}$

$8 = 11$

$9 = \frac{145}{12}$

$c = 15$

$b = \frac{1}{6}$

$a = \frac{\frac{- 7}{6}}{14}$

$8 = 11$

$9 = \frac{145}{12}$

$c = 15$

$b = \frac{1}{6}$

Move the negative in front of the fraction.

$a = \frac{- \frac{7}{6}}{14}$

$8 = 11$

$9 = \frac{145}{12}$

$c = 15$

$b = \frac{1}{6}$

Multiply the numerator by the reciprocal of the denominator.

$a = - \frac{7}{6} \cdot \frac{1}{14}$

$8 = 11$

$9 = \frac{145}{12}$

$c = 15$

$b = \frac{1}{6}$

Cancel the common factor of $7$ .

Move the leading negative in $- \frac{7}{6}$ into the numerator.

$a = \frac{- 7}{6} \cdot \frac{1}{14}$

$8 = 11$

$9 = \frac{145}{12}$

$c = 15$

$b = \frac{1}{6}$

Factor $7$ out of $- 7$ .

$a = \frac{7 (- 1)}{6} \cdot \frac{1}{14}$

$8 = 11$

$9 = \frac{145}{12}$

$c = 15$

$b = \frac{1}{6}$

Factor $7$ out of $14$ .

$a = \frac{7 \cdot - 1}{6} \cdot \frac{1}{7 \cdot 2}$

$8 = 11$

$9 = \frac{145}{12}$

$c = 15$

$b = \frac{1}{6}$

Cancel the common factor.

$a = \frac{7 \cdot - 1}{6} \cdot \frac{1}{7 \cdot 2}$

$8 = 11$

$9 = \frac{145}{12}$

$c = 15$

$b = \frac{1}{6}$

Rewrite the expression.

$a = \frac{- 1}{6} \cdot \frac{1}{2}$

$8 = 11$

$9 = \frac{145}{12}$

$c = 15$

$b = \frac{1}{6}$

$a = \frac{- 1}{6} \cdot \frac{1}{2}$

$8 = 11$

$9 = \frac{145}{12}$

$c = 15$

$b = \frac{1}{6}$

Multiply $\frac{- 1}{6}$ by $\frac{1}{2}$ .

$a = \frac{- 1}{6 \cdot 2}$

$8 = 11$

$9 = \frac{145}{12}$

$c = 15$

$b = \frac{1}{6}$

Simplify the expression.

Multiply $6$ by $2$ .

$a = \frac{- 1}{12}$

$8 = 11$

$9 = \frac{145}{12}$

$c = 15$

$b = \frac{1}{6}$

Move the negative in front of the fraction.

$a = - \frac{1}{12}$

$8 = 11$

$9 = \frac{145}{12}$

$c = 15$

$b = \frac{1}{6}$

$a = - \frac{1}{12}$

$8 = 11$

$9 = \frac{145}{12}$

$c = 15$

$b = \frac{1}{6}$

$a = - \frac{1}{12}$

$8 = 11$

$9 = \frac{145}{12}$

$c = 15$

$b = \frac{1}{6}$

$a = - \frac{1}{12}$

$8 = 11$

$9 = \frac{145}{12}$

$c = 15$

$b = \frac{1}{6}$

$a = - \frac{1}{12}$

$8 = 11$

$9 = \frac{145}{12}$

$c = 15$

$b = \frac{1}{6}$

Since $8 = 11$ is not true, there is no solution.

No solution

Calculate the value of $y$ using each $x$ value in the table and compare this value to the given $y$ value in the table.

Calculate the value of $y$ such that $y = a x^{2} + b$ when $a = 0$ , $b = 0$ , $c = 0$ , and $x = 2$ .

Simplify each term.

Raise $2$ to the power of $2$ .

$y = 0 \cdot 4 + (0) \cdot (2) + 0$

Multiply $0$ by $4$ .

$y = 0 + (0) \cdot (2) + 0$

Multiply $0$ by $2$ .

$y = 0 + 0 + 0$

Simplify by adding numbers.

Add $0$ and $0$ .

$y = 0 + 0$

Add $0$ and $0$ .

$y = 0$

If the table has a quadratic function rule, $y = y$ for the corresponding $x$ value, $x = 2$ . This check does not pass, since $y = 0$ and $y = 15$ . The function rule can\'t be quadratic.

$0 \neq 15$

Since $y \neq y$ for the corresponding $x$ values, the function is not quadratic.

The function is not quadratic

Check if the function rule is cubic.

To find if the table follows a function rule, check whether the function rule could follow the form $y = a x^{3} + b x^{2} + c x + d$ .

$y = a x^{3} + b x^{2} + c x + d$

Build a set of $4$ equations from the table such that $y = a x^{3} + b x^{2} + c x + d$ .

Calculate the values of $a$ , $b$ , $c$ , and $d$ .

Solve for $d$ in $15 = a \cdot 2^{3} + b \cdot 2^{2} + c (2) + d$ .

Rewrite the equation as $a \cdot 2^{3} + b \cdot 2^{2} + c (2) + d = 15$ .

$a \cdot 2^{3} + b \cdot 2^{2} + c (2) + d = 15$

$13 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + d$

$9 = a \cdot 7^{3} + b \cdot 2^{2} + c (2) + d$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

Simplify each term.

Raise $2$ to the power of $3$ .

$a \cdot 8 + b \cdot 2^{2} + c (2) + d = 15$

$13 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + d$

$9 = a \cdot 7^{3} + b \cdot 2^{2} + c (2) + d$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

Move $8$ to the left of $a$ .

$8 \cdot a + b \cdot 2^{2} + c (2) + d = 15$

$13 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + d$

$9 = a \cdot 7^{3} + b \cdot 2^{2} + c (2) + d$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

Raise $2$ to the power of $2$ .

$8 a + b \cdot 4 + c (2) + d = 15$

$13 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + d$

$9 = a \cdot 7^{3} + b \cdot 2^{2} + c (2) + d$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

Move $4$ to the left of $b$ .

$8 a + 4 \cdot b + c (2) + d = 15$

$13 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + d$

$9 = a \cdot 7^{3} + b \cdot 2^{2} + c (2) + d$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

Move $2$ to the left of $c$ .

$8 a + 4 b + 2 c + d = 15$

$13 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + d$

$9 = a \cdot 7^{3} + b \cdot 2^{2} + c (2) + d$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

$8 a + 4 b + 2 c + d = 15$

$13 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + d$

$9 = a \cdot 7^{3} + b \cdot 2^{2} + c (2) + d$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

Move all terms not containing $d$ to the right side of the equation.

Subtract $8 a$ from both sides of the equation.

$4 b + 2 c + d = 15 - 8 a$

$13 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + d$

$9 = a \cdot 7^{3} + b \cdot 2^{2} + c (2) + d$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

Subtract $4 b$ from both sides of the equation.

$2 c + d = 15 - 8 a - 4 b$

$13 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + d$

$9 = a \cdot 7^{3} + b \cdot 2^{2} + c (2) + d$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

Subtract $2 c$ from both sides of the equation.

$d = 15 - 8 a - 4 b - 2 c$

$13 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + d$

$9 = a \cdot 7^{3} + b \cdot 2^{2} + c (2) + d$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

$d = 15 - 8 a - 4 b - 2 c$

$13 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + d$

$9 = a \cdot 7^{3} + b \cdot 2^{2} + c (2) + d$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

$d = 15 - 8 a - 4 b - 2 c$

$13 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + d$

$9 = a \cdot 7^{3} + b \cdot 2^{2} + c (2) + d$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

Replace all occurrences of $d$ with $15 - 8 a - 4 b - 2 c$ in each equation.

Replace all occurrences of $d$ in $13 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + d$ with $15 - 8 a - 4 b - 2 c$ .

$13 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + 15 - 8 a - 4 b - 2 c$

$d = 15 - 8 a - 4 b - 2 c$

$9 = a \cdot 7^{3} + b \cdot 2^{2} + c (2) + d$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

Simplify $13 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + 15 - 8 a - 4 b - 2 c$ .

Simplify the left side.

Remove parentheses.

$13 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + 15 - 8 a - 4 b - 2 c$

$d = 15 - 8 a - 4 b - 2 c$

$9 = a \cdot 7^{3} + b \cdot 2^{2} + c (2) + d$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

$13 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + 15 - 8 a - 4 b - 2 c$

$d = 15 - 8 a - 4 b - 2 c$

$9 = a \cdot 7^{3} + b \cdot 2^{2} + c (2) + d$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

Simplify the right side.

Simplify $a \cdot 6^{3} + b \cdot 2^{2} + c (2) + 15 - 8 a - 4 b - 2 c$ .

Combine the opposite terms in $a \cdot 6^{3} + b \cdot 2^{2} + c (2) + 15 - 8 a - 4 b - 2 c$ .

Reorder the factors in the terms $c (2)$ and $- 2 c$ .

$13 = a \cdot 6^{3} + b \cdot 2^{2} + 2 c + 15 - 8 a - 4 b - 2 c$

$d = 15 - 8 a - 4 b - 2 c$

$9 = a \cdot 7^{3} + b \cdot 2^{2} + c (2) + d$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

Subtract $2 c$ from $2 c$ .

$13 = a \cdot 6^{3} + b \cdot 2^{2} + 15 - 8 a - 4 b + 0$

$d = 15 - 8 a - 4 b - 2 c$

$9 = a \cdot 7^{3} + b \cdot 2^{2} + c (2) + d$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

Add $a \cdot 6^{3} + b \cdot 2^{2} + 15 - 8 a - 4 b$ and $0$ .

$13 = a \cdot 6^{3} + b \cdot 2^{2} + 15 - 8 a - 4 b$

$d = 15 - 8 a - 4 b - 2 c$

$9 = a \cdot 7^{3} + b \cdot 2^{2} + c (2) + d$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

$13 = a \cdot 6^{3} + b \cdot 2^{2} + 15 - 8 a - 4 b$

$d = 15 - 8 a - 4 b - 2 c$

$9 = a \cdot 7^{3} + b \cdot 2^{2} + c (2) + d$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

Simplify each term.

Raise $6$ to the power of $3$ .

$13 = a \cdot 216 + b \cdot 2^{2} + 15 - 8 a - 4 b$

$d = 15 - 8 a - 4 b - 2 c$

$9 = a \cdot 7^{3} + b \cdot 2^{2} + c (2) + d$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

Move $216$ to the left of $a$ .

$13 = 216 \cdot a + b \cdot 2^{2} + 15 - 8 a - 4 b$

$d = 15 - 8 a - 4 b - 2 c$

$9 = a \cdot 7^{3} + b \cdot 2^{2} + c (2) + d$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

Raise $2$ to the power of $2$ .

$13 = 216 a + b \cdot 4 + 15 - 8 a - 4 b$

$d = 15 - 8 a - 4 b - 2 c$

$9 = a \cdot 7^{3} + b \cdot 2^{2} + c (2) + d$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

Move $4$ to the left of $b$ .

$13 = 216 a + 4 b + 15 - 8 a - 4 b$

$d = 15 - 8 a - 4 b - 2 c$

$9 = a \cdot 7^{3} + b \cdot 2^{2} + c (2) + d$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

$13 = 216 a + 4 b + 15 - 8 a - 4 b$

$d = 15 - 8 a - 4 b - 2 c$

$9 = a \cdot 7^{3} + b \cdot 2^{2} + c (2) + d$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

Simplify by adding terms.

Combine the opposite terms in $216 a + 4 b + 15 - 8 a - 4 b$ .

Subtract $4 b$ from $4 b$ .

$13 = 216 a + 15 - 8 a + 0$

$d = 15 - 8 a - 4 b - 2 c$

$9 = a \cdot 7^{3} + b \cdot 2^{2} + c (2) + d$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

Add $216 a + 15 - 8 a$ and $0$ .

$13 = 216 a + 15 - 8 a$

$d = 15 - 8 a - 4 b - 2 c$

$9 = a \cdot 7^{3} + b \cdot 2^{2} + c (2) + d$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

$13 = 216 a + 15 - 8 a$

$d = 15 - 8 a - 4 b - 2 c$

$9 = a \cdot 7^{3} + b \cdot 2^{2} + c (2) + d$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

Subtract $8 a$ from $216 a$ .

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$9 = a \cdot 7^{3} + b \cdot 2^{2} + c (2) + d$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$9 = a \cdot 7^{3} + b \cdot 2^{2} + c (2) + d$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$9 = a \cdot 7^{3} + b \cdot 2^{2} + c (2) + d$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$9 = a \cdot 7^{3} + b \cdot 2^{2} + c (2) + d$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$9 = a \cdot 7^{3} + b \cdot 2^{2} + c (2) + d$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

Replace all occurrences of $d$ in $9 = a \cdot 7^{3} + b \cdot 2^{2} + c (2) + d$ with $15 - 8 a - 4 b - 2 c$ .

$9 = a \cdot 7^{3} + b \cdot 2^{2} + c (2) + 15 - 8 a - 4 b - 2 c$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

Simplify $9 = a \cdot 7^{3} + b \cdot 2^{2} + c (2) + 15 - 8 a - 4 b - 2 c$ .

Simplify the left side.

Remove parentheses.

$9 = a \cdot 7^{3} + b \cdot 2^{2} + c (2) + 15 - 8 a - 4 b - 2 c$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

$9 = a \cdot 7^{3} + b \cdot 2^{2} + c (2) + 15 - 8 a - 4 b - 2 c$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

Simplify the right side.

Simplify $a \cdot 7^{3} + b \cdot 2^{2} + c (2) + 15 - 8 a - 4 b - 2 c$ .

Combine the opposite terms in $a \cdot 7^{3} + b \cdot 2^{2} + c (2) + 15 - 8 a - 4 b - 2 c$ .

Reorder the factors in the terms $c (2)$ and $- 2 c$ .

$9 = a \cdot 7^{3} + b \cdot 2^{2} + 2 c + 15 - 8 a - 4 b - 2 c$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

Subtract $2 c$ from $2 c$ .

$9 = a \cdot 7^{3} + b \cdot 2^{2} + 15 - 8 a - 4 b + 0$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

Add $a \cdot 7^{3} + b \cdot 2^{2} + 15 - 8 a - 4 b$ and $0$ .

$9 = a \cdot 7^{3} + b \cdot 2^{2} + 15 - 8 a - 4 b$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

$9 = a \cdot 7^{3} + b \cdot 2^{2} + 15 - 8 a - 4 b$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

Simplify each term.

Raise $7$ to the power of $3$ .

$9 = a \cdot 343 + b \cdot 2^{2} + 15 - 8 a - 4 b$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

Move $343$ to the left of $a$ .

$9 = 343 \cdot a + b \cdot 2^{2} + 15 - 8 a - 4 b$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

Raise $2$ to the power of $2$ .

$9 = 343 a + b \cdot 4 + 15 - 8 a - 4 b$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

Move $4$ to the left of $b$ .

$9 = 343 a + 4 b + 15 - 8 a - 4 b$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

$9 = 343 a + 4 b + 15 - 8 a - 4 b$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

Simplify by adding terms.

Combine the opposite terms in $343 a + 4 b + 15 - 8 a - 4 b$ .

Subtract $4 b$ from $4 b$ .

$9 = 343 a + 15 - 8 a + 0$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

Add $343 a + 15 - 8 a$ and $0$ .

$9 = 343 a + 15 - 8 a$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

$9 = 343 a + 15 - 8 a$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

Subtract $8 a$ from $343 a$ .

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

Replace all occurrences of $d$ in $8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$ with $15 - 8 a - 4 b - 2 c$ .

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + 15 - 8 a - 4 b - 2 c$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

Simplify $8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + 15 - 8 a - 4 b - 2 c$ .

Simplify the left side.

Remove parentheses.

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + 15 - 8 a - 4 b - 2 c$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + 15 - 8 a - 4 b - 2 c$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

Simplify the right side.

Simplify $a \cdot 8^{3} + b \cdot 2^{2} + c (2) + 15 - 8 a - 4 b - 2 c$ .

Combine the opposite terms in $a \cdot 8^{3} + b \cdot 2^{2} + c (2) + 15 - 8 a - 4 b - 2 c$ .

Reorder the factors in the terms $c (2)$ and $- 2 c$ .

$8 = a \cdot 8^{3} + b \cdot 2^{2} + 2 c + 15 - 8 a - 4 b - 2 c$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

Subtract $2 c$ from $2 c$ .

$8 = a \cdot 8^{3} + b \cdot 2^{2} + 15 - 8 a - 4 b + 0$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

Add $a \cdot 8^{3} + b \cdot 2^{2} + 15 - 8 a - 4 b$ and $0$ .

$8 = a \cdot 8^{3} + b \cdot 2^{2} + 15 - 8 a - 4 b$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

$8 = a \cdot 8^{3} + b \cdot 2^{2} + 15 - 8 a - 4 b$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

Simplify each term.

Raise $8$ to the power of $3$ .

$8 = a \cdot 512 + b \cdot 2^{2} + 15 - 8 a - 4 b$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

Move $512$ to the left of $a$ .

$8 = 512 \cdot a + b \cdot 2^{2} + 15 - 8 a - 4 b$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

Raise $2$ to the power of $2$ .

$8 = 512 a + b \cdot 4 + 15 - 8 a - 4 b$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

Move $4$ to the left of $b$ .

$8 = 512 a + 4 b + 15 - 8 a - 4 b$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

$8 = 512 a + 4 b + 15 - 8 a - 4 b$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

Simplify by adding terms.

Combine the opposite terms in $512 a + 4 b + 15 - 8 a - 4 b$ .

Subtract $4 b$ from $4 b$ .

$8 = 512 a + 15 - 8 a + 0$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

Add $512 a + 15 - 8 a$ and $0$ .

$8 = 512 a + 15 - 8 a$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

$8 = 512 a + 15 - 8 a$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

Subtract $8 a$ from $512 a$ .

$8 = 504 a + 15$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

$8 = 504 a + 15$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

$8 = 504 a + 15$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

$8 = 504 a + 15$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

$8 = 504 a + 15$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$

Replace all occurrences of $d$ in $5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + d$ with $15 - 8 a - 4 b - 2 c$ .

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + 15 - 8 a - 4 b - 2 c$

$8 = 504 a + 15$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

Simplify $5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + 15 - 8 a - 4 b - 2 c$ .

Simplify the left side.

Remove parentheses.

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + 15 - 8 a - 4 b - 2 c$

$8 = 504 a + 15$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + c (2) + 15 - 8 a - 4 b - 2 c$

$8 = 504 a + 15$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

Simplify the right side.

Simplify $a \cdot 12^{3} + b \cdot 2^{2} + c (2) + 15 - 8 a - 4 b - 2 c$ .

Combine the opposite terms in $a \cdot 12^{3} + b \cdot 2^{2} + c (2) + 15 - 8 a - 4 b - 2 c$ .

Reorder the factors in the terms $c (2)$ and $- 2 c$ .

$5 = a \cdot 12^{3} + b \cdot 2^{2} + 2 c + 15 - 8 a - 4 b - 2 c$

$8 = 504 a + 15$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

Subtract $2 c$ from $2 c$ .

$5 = a \cdot 12^{3} + b \cdot 2^{2} + 15 - 8 a - 4 b + 0$

$8 = 504 a + 15$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

Add $a \cdot 12^{3} + b \cdot 2^{2} + 15 - 8 a - 4 b$ and $0$ .

$5 = a \cdot 12^{3} + b \cdot 2^{2} + 15 - 8 a - 4 b$

$8 = 504 a + 15$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$5 = a \cdot 12^{3} + b \cdot 2^{2} + 15 - 8 a - 4 b$

$8 = 504 a + 15$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

Simplify each term.

Raise $12$ to the power of $3$ .

$5 = a \cdot 1728 + b \cdot 2^{2} + 15 - 8 a - 4 b$

$8 = 504 a + 15$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

Move $1728$ to the left of $a$ .

$5 = 1728 \cdot a + b \cdot 2^{2} + 15 - 8 a - 4 b$

$8 = 504 a + 15$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

Raise $2$ to the power of $2$ .

$5 = 1728 a + b \cdot 4 + 15 - 8 a - 4 b$

$8 = 504 a + 15$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

Move $4$ to the left of $b$ .

$5 = 1728 a + 4 b + 15 - 8 a - 4 b$

$8 = 504 a + 15$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$5 = 1728 a + 4 b + 15 - 8 a - 4 b$

$8 = 504 a + 15$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

Simplify by adding terms.

Combine the opposite terms in $1728 a + 4 b + 15 - 8 a - 4 b$ .

Subtract $4 b$ from $4 b$ .

$5 = 1728 a + 15 - 8 a + 0$

$8 = 504 a + 15$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

Add $1728 a + 15 - 8 a$ and $0$ .

$5 = 1728 a + 15 - 8 a$

$8 = 504 a + 15$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$5 = 1728 a + 15 - 8 a$

$8 = 504 a + 15$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

Subtract $8 a$ from $1728 a$ .

$5 = 1720 a + 15$

$8 = 504 a + 15$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$5 = 1720 a + 15$

$8 = 504 a + 15$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$5 = 1720 a + 15$

$8 = 504 a + 15$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$5 = 1720 a + 15$

$8 = 504 a + 15$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$5 = 1720 a + 15$

$8 = 504 a + 15$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$5 = 1720 a + 15$

$8 = 504 a + 15$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

Solve for $a$ in $5 = 1720 a + 15$ .

Rewrite the equation as $1720 a + 15 = 5$ .

$1720 a + 15 = 5$

$8 = 504 a + 15$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

Move all terms not containing $a$ to the right side of the equation.

Subtract $15$ from both sides of the equation.

$1720 a = 5 - 15$

$8 = 504 a + 15$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

Subtract $15$ from $5$ .

$1720 a = - 10$

$8 = 504 a + 15$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$1720 a = - 10$

$8 = 504 a + 15$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

Divide each term in $1720 a = - 10$ by $1720$ and simplify.

Divide each term in $1720 a = - 10$ by $1720$ .

$\frac{1720 a}{1720} = \frac{- 10}{1720}$

$8 = 504 a + 15$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

Simplify the left side.

Cancel the common factor of $1720$ .

Cancel the common factor.

$\frac{1720 a}{1720} = \frac{- 10}{1720}$

$8 = 504 a + 15$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

Divide $a$ by $1$ .

$a = \frac{- 10}{1720}$

$8 = 504 a + 15$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$a = \frac{- 10}{1720}$

$8 = 504 a + 15$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$a = \frac{- 10}{1720}$

$8 = 504 a + 15$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

Simplify the right side.

Cancel the common factor of $- 10$ and $1720$ .

Factor $10$ out of $- 10$ .

$a = \frac{10 (- 1)}{1720}$

$8 = 504 a + 15$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

Cancel the common factors.

Factor $10$ out of $1720$ .

$a = \frac{10 \cdot - 1}{10 \cdot 172}$

$8 = 504 a + 15$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

Cancel the common factor.

$a = \frac{10 \cdot - 1}{10 \cdot 172}$

$8 = 504 a + 15$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

Rewrite the expression.

$a = \frac{- 1}{172}$

$8 = 504 a + 15$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$a = \frac{- 1}{172}$

$8 = 504 a + 15$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$a = \frac{- 1}{172}$

$8 = 504 a + 15$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

Move the negative in front of the fraction.

$a = - \frac{1}{172}$

$8 = 504 a + 15$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$a = - \frac{1}{172}$

$8 = 504 a + 15$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$a = - \frac{1}{172}$

$8 = 504 a + 15$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$a = - \frac{1}{172}$

$8 = 504 a + 15$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

Replace all occurrences of $a$ with $- \frac{1}{172}$ in each equation.

Replace all occurrences of $a$ in $8 = 504 a + 15$ with $- \frac{1}{172}$ .

$8 = 504 (- \frac{1}{172}) + 15$

$a = - \frac{1}{172}$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

Simplify the right side.

Simplify $504 (- \frac{1}{172}) + 15$ .

Simplify each term.

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{1}{172}$ into the numerator.

$8 = 504 (\frac{- 1}{172}) + 15$

$a = - \frac{1}{172}$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

Factor $4$ out of $504$ .

$8 = 4 (126) (\frac{- 1}{172}) + 15$

$a = - \frac{1}{172}$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

Factor $4$ out of $172$ .

$8 = 4 \cdot (126 (\frac{- 1}{4 \cdot 43})) + 15$

$a = - \frac{1}{172}$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

Cancel the common factor.

$8 = 4 \cdot (126 (\frac{- 1}{4 \cdot 43})) + 15$

$a = - \frac{1}{172}$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

Rewrite the expression.

$8 = 126 (\frac{- 1}{43}) + 15$

$a = - \frac{1}{172}$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$8 = 126 (\frac{- 1}{43}) + 15$

$a = - \frac{1}{172}$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

Combine $126$ and $\frac{- 1}{43}$ .

$8 = \frac{126 \cdot - 1}{43} + 15$

$a = - \frac{1}{172}$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

Multiply $126$ by $- 1$ .

$8 = \frac{- 126}{43} + 15$

$a = - \frac{1}{172}$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

Move the negative in front of the fraction.

$8 = - \frac{126}{43} + 15$

$a = - \frac{1}{172}$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$8 = - \frac{126}{43} + 15$

$a = - \frac{1}{172}$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

To write $15$ as a fraction with a common denominator, multiply by $\frac{43}{43}$ .

$8 = - \frac{126}{43} + 15 \cdot \frac{43}{43}$

$a = - \frac{1}{172}$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

Combine $15$ and $\frac{43}{43}$ .

$8 = - \frac{126}{43} + \frac{15 \cdot 43}{43}$

$a = - \frac{1}{172}$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

Combine the numerators over the common denominator.

$8 = \frac{- 126 + 15 \cdot 43}{43}$

$a = - \frac{1}{172}$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

Simplify the numerator.

Multiply $15$ by $43$ .

$8 = \frac{- 126 + 645}{43}$

$a = - \frac{1}{172}$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

Add $- 126$ and $645$ .

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

$9 = 335 a + 15$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

Replace all occurrences of $a$ in $9 = 335 a + 15$ with $- \frac{1}{172}$ .

$9 = 335 (- \frac{1}{172}) + 15$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

Simplify the right side.

Simplify $335 (- \frac{1}{172}) + 15$ .

Simplify each term.

Multiply $335 (- \frac{1}{172})$ .

Multiply $- 1$ by $335$ .

$9 = - 335 (\frac{1}{172}) + 15$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

Combine $- 335$ and $\frac{1}{172}$ .

$9 = \frac{- 335}{172} + 15$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$9 = \frac{- 335}{172} + 15$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

Move the negative in front of the fraction.

$9 = - \frac{335}{172} + 15$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$9 = - \frac{335}{172} + 15$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

To write $15$ as a fraction with a common denominator, multiply by $\frac{172}{172}$ .

$9 = - \frac{335}{172} + 15 \cdot \frac{172}{172}$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

Combine $15$ and $\frac{172}{172}$ .

$9 = - \frac{335}{172} + \frac{15 \cdot 172}{172}$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

Combine the numerators over the common denominator.

$9 = \frac{- 335 + 15 \cdot 172}{172}$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

Simplify the numerator.

Multiply $15$ by $172$ .

$9 = \frac{- 335 + 2580}{172}$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

Add $- 335$ and $2580$ .

$9 = \frac{2245}{172}$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$9 = \frac{2245}{172}$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$9 = \frac{2245}{172}$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

$9 = \frac{2245}{172}$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

$13 = 208 a + 15$

$d = 15 - 8 a - 4 b - 2 c$

Replace all occurrences of $a$ in $13 = 208 a + 15$ with $- \frac{1}{172}$ .

$13 = 208 (- \frac{1}{172}) + 15$

$9 = \frac{2245}{172}$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

$d = 15 - 8 a - 4 b - 2 c$

Simplify the right side.

Simplify $208 (- \frac{1}{172}) + 15$ .

Simplify each term.

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{1}{172}$ into the numerator.

$13 = 208 (\frac{- 1}{172}) + 15$

$9 = \frac{2245}{172}$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

$d = 15 - 8 a - 4 b - 2 c$

Factor $4$ out of $208$ .

$13 = 4 (52) (\frac{- 1}{172}) + 15$

$9 = \frac{2245}{172}$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

$d = 15 - 8 a - 4 b - 2 c$

Factor $4$ out of $172$ .

$13 = 4 \cdot (52 (\frac{- 1}{4 \cdot 43})) + 15$

$9 = \frac{2245}{172}$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

$d = 15 - 8 a - 4 b - 2 c$

Cancel the common factor.

$13 = 4 \cdot (52 (\frac{- 1}{4 \cdot 43})) + 15$

$9 = \frac{2245}{172}$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

$d = 15 - 8 a - 4 b - 2 c$

Rewrite the expression.

$13 = 52 (\frac{- 1}{43}) + 15$

$9 = \frac{2245}{172}$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

$d = 15 - 8 a - 4 b - 2 c$

$13 = 52 (\frac{- 1}{43}) + 15$

$9 = \frac{2245}{172}$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

$d = 15 - 8 a - 4 b - 2 c$

Combine $52$ and $\frac{- 1}{43}$ .

$13 = \frac{52 \cdot - 1}{43} + 15$

$9 = \frac{2245}{172}$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

$d = 15 - 8 a - 4 b - 2 c$

Multiply $52$ by $- 1$ .

$13 = \frac{- 52}{43} + 15$

$9 = \frac{2245}{172}$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

$d = 15 - 8 a - 4 b - 2 c$

Move the negative in front of the fraction.

$13 = - \frac{52}{43} + 15$

$9 = \frac{2245}{172}$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

$d = 15 - 8 a - 4 b - 2 c$

$13 = - \frac{52}{43} + 15$

$9 = \frac{2245}{172}$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

$d = 15 - 8 a - 4 b - 2 c$

To write $15$ as a fraction with a common denominator, multiply by $\frac{43}{43}$ .

$13 = - \frac{52}{43} + 15 \cdot \frac{43}{43}$

$9 = \frac{2245}{172}$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

$d = 15 - 8 a - 4 b - 2 c$

Combine $15$ and $\frac{43}{43}$ .

$13 = - \frac{52}{43} + \frac{15 \cdot 43}{43}$

$9 = \frac{2245}{172}$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

$d = 15 - 8 a - 4 b - 2 c$

Combine the numerators over the common denominator.

$13 = \frac{- 52 + 15 \cdot 43}{43}$

$9 = \frac{2245}{172}$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

$d = 15 - 8 a - 4 b - 2 c$

Simplify the numerator.

Multiply $15$ by $43$ .

$13 = \frac{- 52 + 645}{43}$

$9 = \frac{2245}{172}$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

$d = 15 - 8 a - 4 b - 2 c$

Add $- 52$ and $645$ .

$13 = \frac{593}{43}$

$9 = \frac{2245}{172}$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

$d = 15 - 8 a - 4 b - 2 c$

$13 = \frac{593}{43}$

$9 = \frac{2245}{172}$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

$d = 15 - 8 a - 4 b - 2 c$

$13 = \frac{593}{43}$

$9 = \frac{2245}{172}$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

$d = 15 - 8 a - 4 b - 2 c$

$13 = \frac{593}{43}$

$9 = \frac{2245}{172}$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

$d = 15 - 8 a - 4 b - 2 c$

Replace all occurrences of $a$ in $d = 15 - 8 a - 4 b - 2 c$ with $- \frac{1}{172}$ .

$d = 15 - 8 (- \frac{1}{172}) - 4 b - 2 c$

$13 = \frac{593}{43}$

$9 = \frac{2245}{172}$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

Simplify the right side.

Simplify $15 - 8 (- \frac{1}{172}) - 4 b - 2 c$ .

Simplify each term.

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{1}{172}$ into the numerator.

$d = 15 - 8 (\frac{- 1}{172}) - 4 b - 2 c$

$13 = \frac{593}{43}$

$9 = \frac{2245}{172}$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

Factor $4$ out of $- 8$ .

$d = 15 + 4 (- 2) (\frac{- 1}{172}) - 4 b - 2 c$

$13 = \frac{593}{43}$

$9 = \frac{2245}{172}$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

Factor $4$ out of $172$ .

$d = 15 + 4 \cdot (- 2 \frac{- 1}{4 \cdot 43}) - 4 b - 2 c$

$13 = \frac{593}{43}$

$9 = \frac{2245}{172}$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

Cancel the common factor.

$d = 15 + 4 \cdot (- 2 \frac{- 1}{4 \cdot 43}) - 4 b - 2 c$

$13 = \frac{593}{43}$

$9 = \frac{2245}{172}$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

Rewrite the expression.

$d = 15 - 2 (\frac{- 1}{43}) - 4 b - 2 c$

$13 = \frac{593}{43}$

$9 = \frac{2245}{172}$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

$d = 15 - 2 (\frac{- 1}{43}) - 4 b - 2 c$

$13 = \frac{593}{43}$

$9 = \frac{2245}{172}$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

Combine $- 2$ and $\frac{- 1}{43}$ .

$d = 15 + \frac{- 2 \cdot - 1}{43} - 4 b - 2 c$

$13 = \frac{593}{43}$

$9 = \frac{2245}{172}$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

Multiply $- 2$ by $- 1$ .

$d = 15 + \frac{2}{43} - 4 b - 2 c$

$13 = \frac{593}{43}$

$9 = \frac{2245}{172}$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

$d = 15 + \frac{2}{43} - 4 b - 2 c$

$13 = \frac{593}{43}$

$9 = \frac{2245}{172}$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

To write $15$ as a fraction with a common denominator, multiply by $\frac{43}{43}$ .

$d = 15 \cdot \frac{43}{43} + \frac{2}{43} - 4 b - 2 c$

$13 = \frac{593}{43}$

$9 = \frac{2245}{172}$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

Combine $15$ and $\frac{43}{43}$ .

$d = \frac{15 \cdot 43}{43} + \frac{2}{43} - 4 b - 2 c$

$13 = \frac{593}{43}$

$9 = \frac{2245}{172}$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

Combine the numerators over the common denominator.

$d = \frac{15 \cdot 43 + 2}{43} - 4 b - 2 c$

$13 = \frac{593}{43}$

$9 = \frac{2245}{172}$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

Simplify the numerator.

Multiply $15$ by $43$ .

$d = \frac{645 + 2}{43} - 4 b - 2 c$

$13 = \frac{593}{43}$

$9 = \frac{2245}{172}$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

Add $645$ and $2$ .

$d = \frac{647}{43} - 4 b - 2 c$

$13 = \frac{593}{43}$

$9 = \frac{2245}{172}$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

$d = \frac{647}{43} - 4 b - 2 c$

$13 = \frac{593}{43}$

$9 = \frac{2245}{172}$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

$d = \frac{647}{43} - 4 b - 2 c$

$13 = \frac{593}{43}$

$9 = \frac{2245}{172}$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

$d = \frac{647}{43} - 4 b - 2 c$

$13 = \frac{593}{43}$

$9 = \frac{2245}{172}$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

$d = \frac{647}{43} - 4 b - 2 c$

$13 = \frac{593}{43}$

$9 = \frac{2245}{172}$

$8 = \frac{519}{43}$

$a = - \frac{1}{172}$

Since $13 = \frac{593}{43}$ is not true, there is no solution.

No solution

Calculate the value of $y$ using each $x$ value in the table and compare this value to the given $y$ value in the table.

Calculate the value of $y$ such that $y = a x^{3} + b$ when $a = 0$ , $b = 0$ , $c = 0$ , $d = 0$ , and $x = 2$ .

Simplify each term.

Raise $2$ to the power of $3$ .

$y = 0 \cdot 8 + (0) \cdot (2^{2}) + (0) \cdot ((2) \cdot 0)$

Multiply $0$ by $8$ .

$y = 0 + (0) \cdot (2^{2}) + (0) \cdot ((2) \cdot 0)$

Raise $2$ to the power of $2$ .

$y = 0 + 0 \cdot 4 + (0) \cdot ((2) \cdot 0)$

Multiply $0$ by $4$ .

$y = 0 + 0 + (0) \cdot ((2) \cdot 0)$

Multiply $2$ by $0$ .

$y = 0 + 0 + 0 \cdot 0$

Multiply $0$ by $0$ .

$y = 0 + 0 + 0$

Simplify by adding numbers.

Add $0$ and $0$ .

$y = 0 + 0$

Add $0$ and $0$ .

$y = 0$

If the table has a cubic function rule, $y = y$ for the corresponding $x$ value, $x = 2$ . This check does not pass, since $y = 0$ and $y = 15$ . The function rule can\'t be cubic.

$0 \neq 15$

Since $y \neq y$ for the corresponding $x$ values, the function is not cubic.

The function is not cubic

There are no values for $a$ , $b$ , $c$ , and $d$ in the equations $y = a x + b$ , $y = a x^{2} + b x + c$ , and $y = a x^{3} + b x^{2} + c x + d$ that work for every pair of $x$ and $y$ .

The table does not have a function rule that is linear, quadratic, or cubic.

Find the Function Rule table[[x,y],[2,15],[6,13],[7,9],[8,8],[12,5]]

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