Find the Function Rule table[[x,y],[1,3],[2,9],[3,27],[4,81],[5,243]]

$\begin{array}{c} x & y \\ 1 & 3 \\ 2 & 9 \\ 3 & 27 \\ 4 & 81 \\ 5 & 243 \end{array}$

Step 1

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 $y = a x + b$ .

$3 = a (1) + b 9 = a (2) + b 27 = a (3) + b 81 = a (4) + b 243 = a (5) + b$

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

Solve for $a$ in $3 = a + b$ .

Rewrite the equation as $a + b = 3$ .

$a + b = 3$

$9 = a (2) + b$

$27 = a (3) + b$

$81 = a (4) + b$

$243 = a (5) + b$

Subtract $b$ from both sides of the equation.

$a = 3 - b$

$9 = a (2) + b$

$27 = a (3) + b$

$81 = a (4) + b$

$243 = a (5) + b$

$a = 3 - b$

$9 = a (2) + b$

$27 = a (3) + b$

$81 = a (4) + b$

$243 = a (5) + b$

Replace all occurrences of $a$ with $3 - b$ in each equation.

Replace all occurrences of $a$ in $9 = a (2) + b$ with $3 - b$ .

$9 = (3 - b) (2) + b$

$a = 3 - b$

$27 = a (3) + b$

$81 = a (4) + b$

$243 = a (5) + b$

Simplify the right side.

Simplify $(3 - b) (2) + b$ .

Simplify each term.

Apply the distributive property.

$9 = 3 \cdot 2 - b \cdot 2 + b$

$a = 3 - b$

$27 = a (3) + b$

$81 = a (4) + b$

$243 = a (5) + b$

Multiply $3$ by $2$ .

$9 = 6 - b \cdot 2 + b$

$a = 3 - b$

$27 = a (3) + b$

$81 = a (4) + b$

$243 = a (5) + b$

Multiply $2$ by $- 1$ .

$9 = 6 - 2 b + b$

$a = 3 - b$

$27 = a (3) + b$

$81 = a (4) + b$

$243 = a (5) + b$

$9 = 6 - 2 b + b$

$a = 3 - b$

$27 = a (3) + b$

$81 = a (4) + b$

$243 = a (5) + b$

Add $- 2 b$ and $b$ .

$9 = 6 - b$

$a = 3 - b$

$27 = a (3) + b$

$81 = a (4) + b$

$243 = a (5) + b$

$9 = 6 - b$

$a = 3 - b$

$27 = a (3) + b$

$81 = a (4) + b$

$243 = a (5) + b$

$9 = 6 - b$

$a = 3 - b$

$27 = a (3) + b$

$81 = a (4) + b$

$243 = a (5) + b$

Replace all occurrences of $a$ in $27 = a (3) + b$ with $3 - b$ .

$27 = (3 - b) (3) + b$

$9 = 6 - b$

$a = 3 - b$

$81 = a (4) + b$

$243 = a (5) + b$

Simplify the right side.

Simplify $(3 - b) (3) + b$ .

Simplify each term.

Apply the distributive property.

$27 = 3 \cdot 3 - b \cdot 3 + b$

$9 = 6 - b$

$a = 3 - b$

$81 = a (4) + b$

$243 = a (5) + b$

Multiply $3$ by $3$ .

$27 = 9 - b \cdot 3 + b$

$9 = 6 - b$

$a = 3 - b$

$81 = a (4) + b$

$243 = a (5) + b$

Multiply $3$ by $- 1$ .

$27 = 9 - 3 b + b$

$9 = 6 - b$

$a = 3 - b$

$81 = a (4) + b$

$243 = a (5) + b$

$27 = 9 - 3 b + b$

$9 = 6 - b$

$a = 3 - b$

$81 = a (4) + b$

$243 = a (5) + b$

Add $- 3 b$ and $b$ .

$27 = 9 - 2 b$

$9 = 6 - b$

$a = 3 - b$

$81 = a (4) + b$

$243 = a (5) + b$

$27 = 9 - 2 b$

$9 = 6 - b$

$a = 3 - b$

$81 = a (4) + b$

$243 = a (5) + b$

$27 = 9 - 2 b$

$9 = 6 - b$

$a = 3 - b$

$81 = a (4) + b$

$243 = a (5) + b$

Replace all occurrences of $a$ in $81 = a (4) + b$ with $3 - b$ .

$81 = (3 - b) (4) + b$

$27 = 9 - 2 b$

$9 = 6 - b$

$a = 3 - b$

$243 = a (5) + b$

Simplify the right side.

Simplify $(3 - b) (4) + b$ .

Simplify each term.

Apply the distributive property.

$81 = 3 \cdot 4 - b \cdot 4 + b$

$27 = 9 - 2 b$

$9 = 6 - b$

$a = 3 - b$

$243 = a (5) + b$

Multiply $3$ by $4$ .

$81 = 12 - b \cdot 4 + b$

$27 = 9 - 2 b$

$9 = 6 - b$

$a = 3 - b$

$243 = a (5) + b$

Multiply $4$ by $- 1$ .

$81 = 12 - 4 b + b$

$27 = 9 - 2 b$

$9 = 6 - b$

$a = 3 - b$

$243 = a (5) + b$

$81 = 12 - 4 b + b$

$27 = 9 - 2 b$

$9 = 6 - b$

$a = 3 - b$

$243 = a (5) + b$

Add $- 4 b$ and $b$ .

$81 = 12 - 3 b$

$27 = 9 - 2 b$

$9 = 6 - b$

$a = 3 - b$

$243 = a (5) + b$

$81 = 12 - 3 b$

$27 = 9 - 2 b$

$9 = 6 - b$

$a = 3 - b$

$243 = a (5) + b$

$81 = 12 - 3 b$

$27 = 9 - 2 b$

$9 = 6 - b$

$a = 3 - b$

$243 = a (5) + b$

Replace all occurrences of $a$ in $243 = a (5) + b$ with $3 - b$ .

$243 = (3 - b) (5) + b$

$81 = 12 - 3 b$

$27 = 9 - 2 b$

$9 = 6 - b$

$a = 3 - b$

Simplify the right side.

Simplify $(3 - b) (5) + b$ .

Simplify each term.

Apply the distributive property.

$243 = 3 \cdot 5 - b \cdot 5 + b$

$81 = 12 - 3 b$

$27 = 9 - 2 b$

$9 = 6 - b$

$a = 3 - b$

Multiply $3$ by $5$ .

$243 = 15 - b \cdot 5 + b$

$81 = 12 - 3 b$

$27 = 9 - 2 b$

$9 = 6 - b$

$a = 3 - b$

Multiply $5$ by $- 1$ .

$243 = 15 - 5 b + b$

$81 = 12 - 3 b$

$27 = 9 - 2 b$

$9 = 6 - b$

$a = 3 - b$

$243 = 15 - 5 b + b$

$81 = 12 - 3 b$

$27 = 9 - 2 b$

$9 = 6 - b$

$a = 3 - b$

Add $- 5 b$ and $b$ .

$243 = 15 - 4 b$

$81 = 12 - 3 b$

$27 = 9 - 2 b$

$9 = 6 - b$

$a = 3 - b$

$243 = 15 - 4 b$

$81 = 12 - 3 b$

$27 = 9 - 2 b$

$9 = 6 - b$

$a = 3 - b$

$243 = 15 - 4 b$

$81 = 12 - 3 b$

$27 = 9 - 2 b$

$9 = 6 - b$

$a = 3 - b$

$243 = 15 - 4 b$

$81 = 12 - 3 b$

$27 = 9 - 2 b$

$9 = 6 - b$

$a = 3 - b$

Solve for $b$ in $243 = 15 - 4 b$ .

Rewrite the equation as $15 - 4 b = 243$ .

$15 - 4 b = 243$

$81 = 12 - 3 b$

$27 = 9 - 2 b$

$9 = 6 - b$

$a = 3 - b$

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

Subtract $15$ from both sides of the equation.

$- 4 b = 243 - 15$

$81 = 12 - 3 b$

$27 = 9 - 2 b$

$9 = 6 - b$

$a = 3 - b$

Subtract $15$ from $243$ .

$- 4 b = 228$

$81 = 12 - 3 b$

$27 = 9 - 2 b$

$9 = 6 - b$

$a = 3 - b$

$- 4 b = 228$

$81 = 12 - 3 b$

$27 = 9 - 2 b$

$9 = 6 - b$

$a = 3 - b$

Divide each term in $- 4 b = 228$ by $- 4$ and simplify.

Divide each term in $- 4 b = 228$ by $- 4$ .

$\frac{- 4 b}{- 4} = \frac{228}{- 4}$

$81 = 12 - 3 b$

$27 = 9 - 2 b$

$9 = 6 - b$

$a = 3 - b$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 b}{- 4} = \frac{228}{- 4}$

$81 = 12 - 3 b$

$27 = 9 - 2 b$

$9 = 6 - b$

$a = 3 - b$

Divide $b$ by $1$ .

$b = \frac{228}{- 4}$

$81 = 12 - 3 b$

$27 = 9 - 2 b$

$9 = 6 - b$

$a = 3 - b$

$b = \frac{228}{- 4}$

$81 = 12 - 3 b$

$27 = 9 - 2 b$

$9 = 6 - b$

$a = 3 - b$

$b = \frac{228}{- 4}$

$81 = 12 - 3 b$

$27 = 9 - 2 b$

$9 = 6 - b$

$a = 3 - b$

Simplify the right side.

Divide $228$ by $- 4$ .

$b = - 57$

$81 = 12 - 3 b$

$27 = 9 - 2 b$

$9 = 6 - b$

$a = 3 - b$

$b = - 57$

$81 = 12 - 3 b$

$27 = 9 - 2 b$

$9 = 6 - b$

$a = 3 - b$

$b = - 57$

$81 = 12 - 3 b$

$27 = 9 - 2 b$

$9 = 6 - b$

$a = 3 - b$

$b = - 57$

$81 = 12 - 3 b$

$27 = 9 - 2 b$

$9 = 6 - b$

$a = 3 - b$

Replace all occurrences of $b$ with $- 57$ in each equation.

Replace all occurrences of $b$ in $81 = 12 - 3 b$ with $- 57$ .

$81 = 12 - 3 \cdot - 57$

$b = - 57$

$27 = 9 - 2 b$

$9 = 6 - b$

$a = 3 - b$

Simplify the right side.

Simplify $12 - 3 \cdot - 57$ .

Multiply $- 3$ by $- 57$ .

$81 = 12 + 171$

$b = - 57$

$27 = 9 - 2 b$

$9 = 6 - b$

$a = 3 - b$

Add $12$ and $171$ .

$81 = 183$

$b = - 57$

$27 = 9 - 2 b$

$9 = 6 - b$

$a = 3 - b$

$81 = 183$

$b = - 57$

$27 = 9 - 2 b$

$9 = 6 - b$

$a = 3 - b$

$81 = 183$

$b = - 57$

$27 = 9 - 2 b$

$9 = 6 - b$

$a = 3 - b$

Replace all occurrences of $b$ in $27 = 9 - 2 b$ with $- 57$ .

$27 = 9 - 2 \cdot - 57$

$81 = 183$

$b = - 57$

$9 = 6 - b$

$a = 3 - b$

Simplify the right side.

Simplify $9 - 2 \cdot - 57$ .

Multiply $- 2$ by $- 57$ .

$27 = 9 + 114$

$81 = 183$

$b = - 57$

$9 = 6 - b$

$a = 3 - b$

Add $9$ and $114$ .

$27 = 123$

$81 = 183$

$b = - 57$

$9 = 6 - b$

$a = 3 - b$

$27 = 123$

$81 = 183$

$b = - 57$

$9 = 6 - b$

$a = 3 - b$

$27 = 123$

$81 = 183$

$b = - 57$

$9 = 6 - b$

$a = 3 - b$

Replace all occurrences of $b$ in $9 = 6 - b$ with $- 57$ .

$9 = 6 - (- 57)$

$27 = 123$

$81 = 183$

$b = - 57$

$a = 3 - b$

Simplify the right side.

Simplify $6 - (- 57)$ .

Multiply $- 1$ by $- 57$ .

$9 = 6 + 57$

$27 = 123$

$81 = 183$

$b = - 57$

$a = 3 - b$

Add $6$ and $57$ .

$9 = 63$

$27 = 123$

$81 = 183$

$b = - 57$

$a = 3 - b$

$9 = 63$

$27 = 123$

$81 = 183$

$b = - 57$

$a = 3 - b$

$9 = 63$

$27 = 123$

$81 = 183$

$b = - 57$

$a = 3 - b$

Replace all occurrences of $b$ in $a = 3 - b$ with $- 57$ .

$a = 3 - (- 57)$

$9 = 63$

$27 = 123$

$81 = 183$

$b = - 57$

Simplify the right side.

Simplify $3 - (- 57)$ .

Multiply $- 1$ by $- 57$ .

$a = 3 + 57$

$9 = 63$

$27 = 123$

$81 = 183$

$b = - 57$

Add $3$ and $57$ .

$a = 60$

$9 = 63$

$27 = 123$

$81 = 183$

$b = - 57$

$a = 60$

$9 = 63$

$27 = 123$

$81 = 183$

$b = - 57$

$a = 60$

$9 = 63$

$27 = 123$

$81 = 183$

$b = - 57$

$a = 60$

$9 = 63$

$27 = 123$

$81 = 183$

$b = - 57$

Since $9 = 63$ 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

Step 2

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 $a$ in $3 = a + b + c$ .

Rewrite the equation as $a + b + c = 3$ .

$a + b + c = 3$

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

$27 = a \cdot 3^{2} + b (3) + c$

$81 = a \cdot 4^{2} + b (4) + c$

$243 = a \cdot 5^{2} + b (5) + c$

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

Subtract $b$ from both sides of the equation.

$a + c = 3 - b$

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

$27 = a \cdot 3^{2} + b (3) + c$

$81 = a \cdot 4^{2} + b (4) + c$

$243 = a \cdot 5^{2} + b (5) + c$

Subtract $c$ from both sides of the equation.

$a = 3 - b - c$

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

$27 = a \cdot 3^{2} + b (3) + c$

$81 = a \cdot 4^{2} + b (4) + c$

$243 = a \cdot 5^{2} + b (5) + c$

$a = 3 - b - c$

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

$27 = a \cdot 3^{2} + b (3) + c$

$81 = a \cdot 4^{2} + b (4) + c$

$243 = a \cdot 5^{2} + b (5) + c$

$a = 3 - b - c$

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

$27 = a \cdot 3^{2} + b (3) + c$

$81 = a \cdot 4^{2} + b (4) + c$

$243 = a \cdot 5^{2} + b (5) + c$

Replace all occurrences of $a$ with $3 - b - c$ in each equation.

Replace all occurrences of $a$ in $9 = a \cdot 2^{2} + b (2) + c$ with $3 - b - c$ .

$9 = (3 - b - c) \cdot 2^{2} + b (2) + c$

$a = 3 - b - c$

$27 = a \cdot 3^{2} + b (3) + c$

$81 = a \cdot 4^{2} + b (4) + c$

$243 = a \cdot 5^{2} + b (5) + c$

Simplify the right side.

Simplify $(3 - b - c) \cdot 2^{2} + b (2) + c$ .

Simplify each term.

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

$9 = (3 - b - c) \cdot 4 + b (2) + c$

$a = 3 - b - c$

$27 = a \cdot 3^{2} + b (3) + c$

$81 = a \cdot 4^{2} + b (4) + c$

$243 = a \cdot 5^{2} + b (5) + c$

Apply the distributive property.

$9 = 3 \cdot 4 - b \cdot 4 - c \cdot 4 + b (2) + c$

$a = 3 - b - c$

$27 = a \cdot 3^{2} + b (3) + c$

$81 = a \cdot 4^{2} + b (4) + c$

$243 = a \cdot 5^{2} + b (5) + c$

Simplify.

Multiply $3$ by $4$ .

$9 = 12 - b \cdot 4 - c \cdot 4 + b (2) + c$

$a = 3 - b - c$

$27 = a \cdot 3^{2} + b (3) + c$

$81 = a \cdot 4^{2} + b (4) + c$

$243 = a \cdot 5^{2} + b (5) + c$

Multiply $4$ by $- 1$ .

$9 = 12 - 4 b - c \cdot 4 + b (2) + c$

$a = 3 - b - c$

$27 = a \cdot 3^{2} + b (3) + c$

$81 = a \cdot 4^{2} + b (4) + c$

$243 = a \cdot 5^{2} + b (5) + c$

Multiply $4$ by $- 1$ .

$9 = 12 - 4 b - 4 c + b (2) + c$

$a = 3 - b - c$

$27 = a \cdot 3^{2} + b (3) + c$

$81 = a \cdot 4^{2} + b (4) + c$

$243 = a \cdot 5^{2} + b (5) + c$

$9 = 12 - 4 b - 4 c + b (2) + c$

$a = 3 - b - c$

$27 = a \cdot 3^{2} + b (3) + c$

$81 = a \cdot 4^{2} + b (4) + c$

$243 = a \cdot 5^{2} + b (5) + c$

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

$9 = 12 - 4 b - 4 c + 2 b + c$

$a = 3 - b - c$

$27 = a \cdot 3^{2} + b (3) + c$

$81 = a \cdot 4^{2} + b (4) + c$

$243 = a \cdot 5^{2} + b (5) + c$

$9 = 12 - 4 b - 4 c + 2 b + c$

$a = 3 - b - c$

$27 = a \cdot 3^{2} + b (3) + c$

$81 = a \cdot 4^{2} + b (4) + c$

$243 = a \cdot 5^{2} + b (5) + c$

Simplify by adding terms.

Add $- 4 b$ and $2 b$ .

$9 = 12 - 2 b - 4 c + c$

$a = 3 - b - c$

$27 = a \cdot 3^{2} + b (3) + c$

$81 = a \cdot 4^{2} + b (4) + c$

$243 = a \cdot 5^{2} + b (5) + c$

Add $- 4 c$ and $c$ .

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$27 = a \cdot 3^{2} + b (3) + c$

$81 = a \cdot 4^{2} + b (4) + c$

$243 = a \cdot 5^{2} + b (5) + c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$27 = a \cdot 3^{2} + b (3) + c$

$81 = a \cdot 4^{2} + b (4) + c$

$243 = a \cdot 5^{2} + b (5) + c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$27 = a \cdot 3^{2} + b (3) + c$

$81 = a \cdot 4^{2} + b (4) + c$

$243 = a \cdot 5^{2} + b (5) + c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$27 = a \cdot 3^{2} + b (3) + c$

$81 = a \cdot 4^{2} + b (4) + c$

$243 = a \cdot 5^{2} + b (5) + c$

Replace all occurrences of $a$ in $27 = a \cdot 3^{2} + b (3) + c$ with $3 - b - c$ .

$27 = (3 - b - c) \cdot 3^{2} + b (3) + c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$81 = a \cdot 4^{2} + b (4) + c$

$243 = a \cdot 5^{2} + b (5) + c$

Simplify the right side.

Simplify $(3 - b - c) \cdot 3^{2} + b (3) + c$ .

Simplify each term.

Raise $3$ to the power of $2$ .

$27 = (3 - b - c) \cdot 9 + b (3) + c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$81 = a \cdot 4^{2} + b (4) + c$

$243 = a \cdot 5^{2} + b (5) + c$

Apply the distributive property.

$27 = 3 \cdot 9 - b \cdot 9 - c \cdot 9 + b (3) + c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$81 = a \cdot 4^{2} + b (4) + c$

$243 = a \cdot 5^{2} + b (5) + c$

Simplify.

Multiply $3$ by $9$ .

$27 = 27 - b \cdot 9 - c \cdot 9 + b (3) + c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$81 = a \cdot 4^{2} + b (4) + c$

$243 = a \cdot 5^{2} + b (5) + c$

Multiply $9$ by $- 1$ .

$27 = 27 - 9 b - c \cdot 9 + b (3) + c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$81 = a \cdot 4^{2} + b (4) + c$

$243 = a \cdot 5^{2} + b (5) + c$

Multiply $9$ by $- 1$ .

$27 = 27 - 9 b - 9 c + b (3) + c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$81 = a \cdot 4^{2} + b (4) + c$

$243 = a \cdot 5^{2} + b (5) + c$

$27 = 27 - 9 b - 9 c + b (3) + c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$81 = a \cdot 4^{2} + b (4) + c$

$243 = a \cdot 5^{2} + b (5) + c$

Move $3$ to the left of $b$ .

$27 = 27 - 9 b - 9 c + 3 b + c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$81 = a \cdot 4^{2} + b (4) + c$

$243 = a \cdot 5^{2} + b (5) + c$

$27 = 27 - 9 b - 9 c + 3 b + c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$81 = a \cdot 4^{2} + b (4) + c$

$243 = a \cdot 5^{2} + b (5) + c$

Simplify by adding terms.

Add $- 9 b$ and $3 b$ .

$27 = 27 - 6 b - 9 c + c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$81 = a \cdot 4^{2} + b (4) + c$

$243 = a \cdot 5^{2} + b (5) + c$

Add $- 9 c$ and $c$ .

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$81 = a \cdot 4^{2} + b (4) + c$

$243 = a \cdot 5^{2} + b (5) + c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$81 = a \cdot 4^{2} + b (4) + c$

$243 = a \cdot 5^{2} + b (5) + c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$81 = a \cdot 4^{2} + b (4) + c$

$243 = a \cdot 5^{2} + b (5) + c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$81 = a \cdot 4^{2} + b (4) + c$

$243 = a \cdot 5^{2} + b (5) + c$

Replace all occurrences of $a$ in $81 = a \cdot 4^{2} + b (4) + c$ with $3 - b - c$ .

$81 = (3 - b - c) \cdot 4^{2} + b (4) + c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$243 = a \cdot 5^{2} + b (5) + c$

Simplify the right side.

Simplify $(3 - b - c) \cdot 4^{2} + b (4) + c$ .

Simplify each term.

Raise $4$ to the power of $2$ .

$81 = (3 - b - c) \cdot 16 + b (4) + c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$243 = a \cdot 5^{2} + b (5) + c$

Apply the distributive property.

$81 = 3 \cdot 16 - b \cdot 16 - c \cdot 16 + b (4) + c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$243 = a \cdot 5^{2} + b (5) + c$

Simplify.

Multiply $3$ by $16$ .

$81 = 48 - b \cdot 16 - c \cdot 16 + b (4) + c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$243 = a \cdot 5^{2} + b (5) + c$

Multiply $16$ by $- 1$ .

$81 = 48 - 16 b - c \cdot 16 + b (4) + c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$243 = a \cdot 5^{2} + b (5) + c$

Multiply $16$ by $- 1$ .

$81 = 48 - 16 b - 16 c + b (4) + c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$243 = a \cdot 5^{2} + b (5) + c$

$81 = 48 - 16 b - 16 c + b (4) + c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$243 = a \cdot 5^{2} + b (5) + c$

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

$81 = 48 - 16 b - 16 c + 4 b + c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$243 = a \cdot 5^{2} + b (5) + c$

$81 = 48 - 16 b - 16 c + 4 b + c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$243 = a \cdot 5^{2} + b (5) + c$

Simplify by adding terms.

Add $- 16 b$ and $4 b$ .

$81 = 48 - 12 b - 16 c + c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$243 = a \cdot 5^{2} + b (5) + c$

Add $- 16 c$ and $c$ .

$81 = 48 - 12 b - 15 c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$243 = a \cdot 5^{2} + b (5) + c$

$81 = 48 - 12 b - 15 c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$243 = a \cdot 5^{2} + b (5) + c$

$81 = 48 - 12 b - 15 c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$243 = a \cdot 5^{2} + b (5) + c$

$81 = 48 - 12 b - 15 c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$243 = a \cdot 5^{2} + b (5) + c$

Replace all occurrences of $a$ in $243 = a \cdot 5^{2} + b (5) + c$ with $3 - b - c$ .

$243 = (3 - b - c) \cdot 5^{2} + b (5) + c$

$81 = 48 - 12 b - 15 c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Simplify the right side.

Simplify $(3 - b - c) \cdot 5^{2} + b (5) + c$ .

Simplify each term.

Raise $5$ to the power of $2$ .

$243 = (3 - b - c) \cdot 25 + b (5) + c$

$81 = 48 - 12 b - 15 c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Apply the distributive property.

$243 = 3 \cdot 25 - b \cdot 25 - c \cdot 25 + b (5) + c$

$81 = 48 - 12 b - 15 c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Simplify.

Multiply $3$ by $25$ .

$243 = 75 - b \cdot 25 - c \cdot 25 + b (5) + c$

$81 = 48 - 12 b - 15 c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Multiply $25$ by $- 1$ .

$243 = 75 - 25 b - c \cdot 25 + b (5) + c$

$81 = 48 - 12 b - 15 c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Multiply $25$ by $- 1$ .

$243 = 75 - 25 b - 25 c + b (5) + c$

$81 = 48 - 12 b - 15 c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$243 = 75 - 25 b - 25 c + b (5) + c$

$81 = 48 - 12 b - 15 c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Move $5$ to the left of $b$ .

$243 = 75 - 25 b - 25 c + 5 b + c$

$81 = 48 - 12 b - 15 c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$243 = 75 - 25 b - 25 c + 5 b + c$

$81 = 48 - 12 b - 15 c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Simplify by adding terms.

Add $- 25 b$ and $5 b$ .

$243 = 75 - 20 b - 25 c + c$

$81 = 48 - 12 b - 15 c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Add $- 25 c$ and $c$ .

$243 = 75 - 20 b - 24 c$

$81 = 48 - 12 b - 15 c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$243 = 75 - 20 b - 24 c$

$81 = 48 - 12 b - 15 c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$243 = 75 - 20 b - 24 c$

$81 = 48 - 12 b - 15 c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$243 = 75 - 20 b - 24 c$

$81 = 48 - 12 b - 15 c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$243 = 75 - 20 b - 24 c$

$81 = 48 - 12 b - 15 c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Solve for $b$ in $243 = 75 - 20 b - 24 c$ .

Rewrite the equation as $75 - 20 b - 24 c = 243$ .

$75 - 20 b - 24 c = 243$

$81 = 48 - 12 b - 15 c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

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

Subtract $75$ from both sides of the equation.

$- 20 b - 24 c = 243 - 75$

$81 = 48 - 12 b - 15 c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Add $24 c$ to both sides of the equation.

$- 20 b = 243 - 75 + 24 c$

$81 = 48 - 12 b - 15 c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Subtract $75$ from $243$ .

$- 20 b = 168 + 24 c$

$81 = 48 - 12 b - 15 c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$- 20 b = 168 + 24 c$

$81 = 48 - 12 b - 15 c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Divide each term in $- 20 b = 168 + 24 c$ by $- 20$ and simplify.

Divide each term in $- 20 b = 168 + 24 c$ by $- 20$ .

$\frac{- 20 b}{- 20} = \frac{168}{- 20} + \frac{24 c}{- 20}$

$81 = 48 - 12 b - 15 c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Simplify the left side.

Cancel the common factor of $- 20$ .

Cancel the common factor.

$\frac{- 20 b}{- 20} = \frac{168}{- 20} + \frac{24 c}{- 20}$

$81 = 48 - 12 b - 15 c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Divide $b$ by $1$ .

$b = \frac{168}{- 20} + \frac{24 c}{- 20}$

$81 = 48 - 12 b - 15 c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$b = \frac{168}{- 20} + \frac{24 c}{- 20}$

$81 = 48 - 12 b - 15 c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$b = \frac{168}{- 20} + \frac{24 c}{- 20}$

$81 = 48 - 12 b - 15 c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Simplify the right side.

Simplify each term.

Cancel the common factor of $168$ and $- 20$ .

Factor $4$ out of $168$ .

$b = \frac{4 (42)}{- 20} + \frac{24 c}{- 20}$

$81 = 48 - 12 b - 15 c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Cancel the common factors.

Factor $4$ out of $- 20$ .

$b = \frac{4 \cdot 42}{4 \cdot - 5} + \frac{24 c}{- 20}$

$81 = 48 - 12 b - 15 c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Cancel the common factor.

$b = \frac{4 \cdot 42}{4 \cdot - 5} + \frac{24 c}{- 20}$

$81 = 48 - 12 b - 15 c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Rewrite the expression.

$b = \frac{42}{- 5} + \frac{24 c}{- 20}$

$81 = 48 - 12 b - 15 c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$b = \frac{42}{- 5} + \frac{24 c}{- 20}$

$81 = 48 - 12 b - 15 c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$b = \frac{42}{- 5} + \frac{24 c}{- 20}$

$81 = 48 - 12 b - 15 c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Move the negative in front of the fraction.

$b = - \frac{42}{5} + \frac{24 c}{- 20}$

$81 = 48 - 12 b - 15 c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Cancel the common factor of $24$ and $- 20$ .

Factor $4$ out of $24 c$ .

$b = - \frac{42}{5} + \frac{4 (6 c)}{- 20}$

$81 = 48 - 12 b - 15 c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Cancel the common factors.

Factor $4$ out of $- 20$ .

$b = - \frac{42}{5} + \frac{4 (6 c)}{4 (- 5)}$

$81 = 48 - 12 b - 15 c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Cancel the common factor.

$b = - \frac{42}{5} + \frac{4 (6 c)}{4 \cdot - 5}$

$81 = 48 - 12 b - 15 c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Rewrite the expression.

$b = - \frac{42}{5} + \frac{6 c}{- 5}$

$81 = 48 - 12 b - 15 c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$b = - \frac{42}{5} + \frac{6 c}{- 5}$

$81 = 48 - 12 b - 15 c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$b = - \frac{42}{5} + \frac{6 c}{- 5}$

$81 = 48 - 12 b - 15 c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Move the negative in front of the fraction.

$b = - \frac{42}{5} - \frac{6 c}{5}$

$81 = 48 - 12 b - 15 c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$81 = 48 - 12 b - 15 c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$81 = 48 - 12 b - 15 c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$81 = 48 - 12 b - 15 c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$81 = 48 - 12 b - 15 c$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Replace all occurrences of $b$ with $- \frac{42}{5} - \frac{6 c}{5}$ in each equation.

Replace all occurrences of $b$ in $81 = 48 - 12 b - 15 c$ with $- \frac{42}{5} - \frac{6 c}{5}$ .

$81 = 48 - 12 (- \frac{42}{5} - \frac{6 c}{5}) - 15 c$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Simplify the right side.

Simplify $48 - 12 (- \frac{42}{5} - \frac{6 c}{5}) - 15 c$ .

Simplify each term.

Apply the distributive property.

$81 = 48 - 12 (- \frac{42}{5}) - 12 (- \frac{6 c}{5}) - 15 c$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Multiply $- 12 (- \frac{42}{5})$ .

Multiply $- 1$ by $- 12$ .

$81 = 48 + 12 (\frac{42}{5}) - 12 (- \frac{6 c}{5}) - 15 c$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Combine $12$ and $\frac{42}{5}$ .

$81 = 48 + \frac{12 \cdot 42}{5} - 12 (- \frac{6 c}{5}) - 15 c$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Multiply $12$ by $42$ .

$81 = 48 + \frac{504}{5} - 12 (- \frac{6 c}{5}) - 15 c$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$81 = 48 + \frac{504}{5} - 12 (- \frac{6 c}{5}) - 15 c$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Multiply $- 12 (- \frac{6 c}{5})$ .

Multiply $- 1$ by $- 12$ .

$81 = 48 + \frac{504}{5} + 12 (\frac{6 c}{5}) - 15 c$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Combine $12$ and $\frac{6 c}{5}$ .

$81 = 48 + \frac{504}{5} + \frac{12 (6 c)}{5} - 15 c$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Multiply $6$ by $12$ .

$81 = 48 + \frac{504}{5} + \frac{72 c}{5} - 15 c$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$81 = 48 + \frac{504}{5} + \frac{72 c}{5} - 15 c$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$81 = 48 + \frac{504}{5} + \frac{72 c}{5} - 15 c$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

To write $48$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$81 = 48 \cdot \frac{5}{5} + \frac{504}{5} + \frac{72 c}{5} - 15 c$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Combine $48$ and $\frac{5}{5}$ .

$81 = \frac{48 \cdot 5}{5} + \frac{504}{5} + \frac{72 c}{5} - 15 c$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Combine the numerators over the common denominator.

$81 = \frac{48 \cdot 5 + 504}{5} + \frac{72 c}{5} - 15 c$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Simplify the numerator.

Multiply $48$ by $5$ .

$81 = \frac{240 + 504}{5} + \frac{72 c}{5} - 15 c$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Add $240$ and $504$ .

$81 = \frac{744}{5} + \frac{72 c}{5} - 15 c$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$81 = \frac{744}{5} + \frac{72 c}{5} - 15 c$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

To write $- 15 c$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$81 = \frac{744}{5} + \frac{72 c}{5} - 15 c \cdot \frac{5}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Combine $- 15 c$ and $\frac{5}{5}$ .

$81 = \frac{744}{5} + \frac{72 c}{5} + \frac{- 15 c \cdot 5}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Combine the numerators over the common denominator.

$81 = \frac{744}{5} + \frac{72 c - 15 c \cdot 5}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Combine the numerators over the common denominator.

$81 = \frac{744 + 72 c - 15 c \cdot 5}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Multiply $5$ by $- 15$ .

$81 = \frac{744 + 72 c - 75 c}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Subtract $75 c$ from $72 c$ .

$81 = \frac{744 - 3 c}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Factor $3$ out of $744 - 3 c$ .

Factor $3$ out of $744$ .

$81 = \frac{3 (248) - 3 c}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Factor $3$ out of $- 3 c$ .

$81 = \frac{3 (248) + 3 (- c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Factor $3$ out of $3 (248) + 3 (- c)$ .

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$27 = 27 - 6 b - 8 c$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Replace all occurrences of $b$ in $27 = 27 - 6 b - 8 c$ with $- \frac{42}{5} - \frac{6 c}{5}$ .

$27 = 27 - 6 (- \frac{42}{5} - \frac{6 c}{5}) - 8 c$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Simplify the right side.

Simplify $27 - 6 (- \frac{42}{5} - \frac{6 c}{5}) - 8 c$ .

Simplify each term.

Apply the distributive property.

$27 = 27 - 6 (- \frac{42}{5}) - 6 (- \frac{6 c}{5}) - 8 c$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Multiply $- 6 (- \frac{42}{5})$ .

Multiply $- 1$ by $- 6$ .

$27 = 27 + 6 (\frac{42}{5}) - 6 (- \frac{6 c}{5}) - 8 c$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Combine $6$ and $\frac{42}{5}$ .

$27 = 27 + \frac{6 \cdot 42}{5} - 6 (- \frac{6 c}{5}) - 8 c$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Multiply $6$ by $42$ .

$27 = 27 + \frac{252}{5} - 6 (- \frac{6 c}{5}) - 8 c$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$27 = 27 + \frac{252}{5} - 6 (- \frac{6 c}{5}) - 8 c$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Multiply $- 6 (- \frac{6 c}{5})$ .

Multiply $- 1$ by $- 6$ .

$27 = 27 + \frac{252}{5} + 6 (\frac{6 c}{5}) - 8 c$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Combine $6$ and $\frac{6 c}{5}$ .

$27 = 27 + \frac{252}{5} + \frac{6 (6 c)}{5} - 8 c$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Multiply $6$ by $6$ .

$27 = 27 + \frac{252}{5} + \frac{36 c}{5} - 8 c$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$27 = 27 + \frac{252}{5} + \frac{36 c}{5} - 8 c$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$27 = 27 + \frac{252}{5} + \frac{36 c}{5} - 8 c$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

To write $27$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$27 = 27 \cdot \frac{5}{5} + \frac{252}{5} + \frac{36 c}{5} - 8 c$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Combine $27$ and $\frac{5}{5}$ .

$27 = \frac{27 \cdot 5}{5} + \frac{252}{5} + \frac{36 c}{5} - 8 c$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Combine the numerators over the common denominator.

$27 = \frac{27 \cdot 5 + 252}{5} + \frac{36 c}{5} - 8 c$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Simplify the numerator.

Multiply $27$ by $5$ .

$27 = \frac{135 + 252}{5} + \frac{36 c}{5} - 8 c$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Add $135$ and $252$ .

$27 = \frac{387}{5} + \frac{36 c}{5} - 8 c$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$27 = \frac{387}{5} + \frac{36 c}{5} - 8 c$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

To write $- 8 c$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$27 = \frac{387}{5} + \frac{36 c}{5} - 8 c \cdot \frac{5}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Combine $- 8 c$ and $\frac{5}{5}$ .

$27 = \frac{387}{5} + \frac{36 c}{5} + \frac{- 8 c \cdot 5}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Combine the numerators over the common denominator.

$27 = \frac{387}{5} + \frac{36 c - 8 c \cdot 5}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Combine the numerators over the common denominator.

$27 = \frac{387 + 36 c - 8 c \cdot 5}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Multiply $5$ by $- 8$ .

$27 = \frac{387 + 36 c - 40 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Subtract $40 c$ from $36 c$ .

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$9 = 12 - 2 b - 3 c$

$a = 3 - b - c$

Replace all occurrences of $b$ in $9 = 12 - 2 b - 3 c$ with $- \frac{42}{5} - \frac{6 c}{5}$ .

$9 = 12 - 2 (- \frac{42}{5} - \frac{6 c}{5}) - 3 c$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$a = 3 - b - c$

Simplify the right side.

Simplify $12 - 2 (- \frac{42}{5} - \frac{6 c}{5}) - 3 c$ .

Simplify each term.

Apply the distributive property.

$9 = 12 - 2 (- \frac{42}{5}) - 2 (- \frac{6 c}{5}) - 3 c$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$a = 3 - b - c$

Multiply $- 2 (- \frac{42}{5})$ .

Multiply $- 1$ by $- 2$ .

$9 = 12 + 2 (\frac{42}{5}) - 2 (- \frac{6 c}{5}) - 3 c$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$a = 3 - b - c$

Combine $2$ and $\frac{42}{5}$ .

$9 = 12 + \frac{2 \cdot 42}{5} - 2 (- \frac{6 c}{5}) - 3 c$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$a = 3 - b - c$

Multiply $2$ by $42$ .

$9 = 12 + \frac{84}{5} - 2 (- \frac{6 c}{5}) - 3 c$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$a = 3 - b - c$

$9 = 12 + \frac{84}{5} - 2 (- \frac{6 c}{5}) - 3 c$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$a = 3 - b - c$

Multiply $- 2 (- \frac{6 c}{5})$ .

Multiply $- 1$ by $- 2$ .

$9 = 12 + \frac{84}{5} + 2 (\frac{6 c}{5}) - 3 c$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$a = 3 - b - c$

Combine $2$ and $\frac{6 c}{5}$ .

$9 = 12 + \frac{84}{5} + \frac{2 (6 c)}{5} - 3 c$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$a = 3 - b - c$

Multiply $6$ by $2$ .

$9 = 12 + \frac{84}{5} + \frac{12 c}{5} - 3 c$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$a = 3 - b - c$

$9 = 12 + \frac{84}{5} + \frac{12 c}{5} - 3 c$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$a = 3 - b - c$

$9 = 12 + \frac{84}{5} + \frac{12 c}{5} - 3 c$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$a = 3 - b - c$

To write $12$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$9 = 12 \cdot \frac{5}{5} + \frac{84}{5} + \frac{12 c}{5} - 3 c$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$a = 3 - b - c$

Combine $12$ and $\frac{5}{5}$ .

$9 = \frac{12 \cdot 5}{5} + \frac{84}{5} + \frac{12 c}{5} - 3 c$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$a = 3 - b - c$

Combine the numerators over the common denominator.

$9 = \frac{12 \cdot 5 + 84}{5} + \frac{12 c}{5} - 3 c$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$a = 3 - b - c$

Simplify the numerator.

Multiply $12$ by $5$ .

$9 = \frac{60 + 84}{5} + \frac{12 c}{5} - 3 c$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$a = 3 - b - c$

Add $60$ and $84$ .

$9 = \frac{144}{5} + \frac{12 c}{5} - 3 c$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$a = 3 - b - c$

$9 = \frac{144}{5} + \frac{12 c}{5} - 3 c$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$a = 3 - b - c$

To write $- 3 c$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$9 = \frac{144}{5} + \frac{12 c}{5} - 3 c \cdot \frac{5}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$a = 3 - b - c$

Combine $- 3 c$ and $\frac{5}{5}$ .

$9 = \frac{144}{5} + \frac{12 c}{5} + \frac{- 3 c \cdot 5}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$a = 3 - b - c$

Combine the numerators over the common denominator.

$9 = \frac{144}{5} + \frac{12 c - 3 c \cdot 5}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$a = 3 - b - c$

Combine the numerators over the common denominator.

$9 = \frac{144 + 12 c - 3 c \cdot 5}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$a = 3 - b - c$

Multiply $5$ by $- 3$ .

$9 = \frac{144 + 12 c - 15 c}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$a = 3 - b - c$

Subtract $15 c$ from $12 c$ .

$9 = \frac{144 - 3 c}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$a = 3 - b - c$

Factor $3$ out of $144 - 3 c$ .

Factor $3$ out of $144$ .

$9 = \frac{3 (48) - 3 c}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$a = 3 - b - c$

Factor $3$ out of $- 3 c$ .

$9 = \frac{3 (48) + 3 (- c)}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$a = 3 - b - c$

Factor $3$ out of $3 (48) + 3 (- c)$ .

$9 = \frac{3 (48 - c)}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$a = 3 - b - c$

$9 = \frac{3 (48 - c)}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$a = 3 - b - c$

$9 = \frac{3 (48 - c)}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$a = 3 - b - c$

$9 = \frac{3 (48 - c)}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$a = 3 - b - c$

Replace all occurrences of $b$ in $a = 3 - b - c$ with $- \frac{42}{5} - \frac{6 c}{5}$ .

$a = 3 - (- \frac{42}{5} - \frac{6 c}{5}) - c$

$9 = \frac{3 (48 - c)}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

Simplify the right side.

Simplify $3 - (- \frac{42}{5} - \frac{6 c}{5}) - c$ .

Simplify each term.

Apply the distributive property.

$a = 3 + \frac{42}{5} + \frac{6 c}{5} - c$

$9 = \frac{3 (48 - c)}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

Multiply $- - \frac{42}{5}$ .

Multiply $- 1$ by $- 1$ .

$a = 3 + 1 (\frac{42}{5}) + \frac{6 c}{5} - c$

$9 = \frac{3 (48 - c)}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

Multiply $\frac{42}{5}$ by $1$ .

$a = 3 + \frac{42}{5} + \frac{6 c}{5} - c$

$9 = \frac{3 (48 - c)}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$a = 3 + \frac{42}{5} + \frac{6 c}{5} - c$

$9 = \frac{3 (48 - c)}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

Multiply $- - \frac{6 c}{5}$ .

Multiply $- 1$ by $- 1$ .

$a = 3 + \frac{42}{5} + 1 (\frac{6 c}{5}) - c$

$9 = \frac{3 (48 - c)}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

Multiply $\frac{6 c}{5}$ by $1$ .

$a = 3 + \frac{42}{5} + \frac{6 c}{5} - c$

$9 = \frac{3 (48 - c)}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$a = 3 + \frac{42}{5} + \frac{6 c}{5} - c$

$9 = \frac{3 (48 - c)}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$a = 3 + \frac{42}{5} + \frac{6 c}{5} - c$

$9 = \frac{3 (48 - c)}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

To write $3$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$a = 3 \cdot \frac{5}{5} + \frac{42}{5} + \frac{6 c}{5} - c$

$9 = \frac{3 (48 - c)}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

Combine $3$ and $\frac{5}{5}$ .

$a = \frac{3 \cdot 5}{5} + \frac{42}{5} + \frac{6 c}{5} - c$

$9 = \frac{3 (48 - c)}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

Combine the numerators over the common denominator.

$a = \frac{3 \cdot 5 + 42}{5} + \frac{6 c}{5} - c$

$9 = \frac{3 (48 - c)}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

Simplify the numerator.

Multiply $3$ by $5$ .

$a = \frac{15 + 42}{5} + \frac{6 c}{5} - c$

$9 = \frac{3 (48 - c)}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

Add $15$ and $42$ .

$a = \frac{57}{5} + \frac{6 c}{5} - c$

$9 = \frac{3 (48 - c)}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$a = \frac{57}{5} + \frac{6 c}{5} - c$

$9 = \frac{3 (48 - c)}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

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

$a = \frac{57}{5} + \frac{6 c}{5} - c \cdot \frac{5}{5}$

$9 = \frac{3 (48 - c)}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

Combine $- c$ and $\frac{5}{5}$ .

$a = \frac{57}{5} + \frac{6 c}{5} + \frac{- c \cdot 5}{5}$

$9 = \frac{3 (48 - c)}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

Combine the numerators over the common denominator.

$a = \frac{57}{5} + \frac{6 c - c \cdot 5}{5}$

$9 = \frac{3 (48 - c)}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

Combine the numerators over the common denominator.

$a = \frac{57 + 6 c - c \cdot 5}{5}$

$9 = \frac{3 (48 - c)}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

Multiply $5$ by $- 1$ .

$a = \frac{57 + 6 c - 5 c}{5}$

$9 = \frac{3 (48 - c)}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

Subtract $5 c$ from $6 c$ .

$a = \frac{57 + c}{5}$

$9 = \frac{3 (48 - c)}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$a = \frac{57 + c}{5}$

$9 = \frac{3 (48 - c)}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$a = \frac{57 + c}{5}$

$9 = \frac{3 (48 - c)}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$a = \frac{57 + c}{5}$

$9 = \frac{3 (48 - c)}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

Solve for $c$ in $9 = \frac{3 (48 - c)}{5}$ .

Rewrite the equation as $\frac{3 (48 - c)}{5} = 9$ .

$\frac{3 (48 - c)}{5} = 9$

$a = \frac{57 + c}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

Multiply both sides by $5$ .

$\frac{3 (48 - c)}{5} \cdot 5 = 9 \cdot 5$

$a = \frac{57 + c}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

Simplify.

Simplify the left side.

Simplify $\frac{3 (48 - c)}{5} \cdot 5$ .

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{3 (48 - c)}{5} \cdot 5 = 9 \cdot 5$

$a = \frac{57 + c}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

Rewrite the expression.

$3 (48 - c) = 9 \cdot 5$

$a = \frac{57 + c}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$3 (48 - c) = 9 \cdot 5$

$a = \frac{57 + c}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

Apply the distributive property.

$3 \cdot 48 + 3 (- c) = 9 \cdot 5$

$a = \frac{57 + c}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

Simplify the expression.

Multiply $3$ by $48$ .

$144 + 3 (- c) = 9 \cdot 5$

$a = \frac{57 + c}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

Multiply $- 1$ by $3$ .

$144 - 3 c = 9 \cdot 5$

$a = \frac{57 + c}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

Reorder $144$ and $- 3 c$ .

$- 3 c + 144 = 9 \cdot 5$

$a = \frac{57 + c}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$- 3 c + 144 = 9 \cdot 5$

$a = \frac{57 + c}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$- 3 c + 144 = 9 \cdot 5$

$a = \frac{57 + c}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$- 3 c + 144 = 9 \cdot 5$

$a = \frac{57 + c}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

Simplify the right side.

Multiply $9$ by $5$ .

$- 3 c + 144 = 45$

$a = \frac{57 + c}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$- 3 c + 144 = 45$

$a = \frac{57 + c}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$- 3 c + 144 = 45$

$a = \frac{57 + c}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

Solve for $c$ .

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

Subtract $144$ from both sides of the equation.

$- 3 c = 45 - 144$

$a = \frac{57 + c}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

Subtract $144$ from $45$ .

$- 3 c = - 99$

$a = \frac{57 + c}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$- 3 c = - 99$

$a = \frac{57 + c}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

Divide each term in $- 3 c = - 99$ by $- 3$ and simplify.

Divide each term in $- 3 c = - 99$ by $- 3$ .

$\frac{- 3 c}{- 3} = \frac{- 99}{- 3}$

$a = \frac{57 + c}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 c}{- 3} = \frac{- 99}{- 3}$

$a = \frac{57 + c}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

Divide $c$ by $1$ .

$c = \frac{- 99}{- 3}$

$a = \frac{57 + c}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$c = \frac{- 99}{- 3}$

$a = \frac{57 + c}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$c = \frac{- 99}{- 3}$

$a = \frac{57 + c}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

Simplify the right side.

Divide $- 99$ by $- 3$ .

$c = 33$

$a = \frac{57 + c}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$c = 33$

$a = \frac{57 + c}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$c = 33$

$a = \frac{57 + c}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$c = 33$

$a = \frac{57 + c}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$c = 33$

$a = \frac{57 + c}{5}$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

Replace all occurrences of $c$ with $33$ in each equation.

Replace all occurrences of $c$ in $a = \frac{57 + c}{5}$ with $33$ .

$a = \frac{57 + 33}{5}$

$c = 33$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

Simplify $a = \frac{57 + 33}{5}$ .

Simplify the left side.

Remove parentheses.

$a = \frac{57 + 33}{5}$

$c = 33$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$a = \frac{57 + 33}{5}$

$c = 33$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

Simplify the right side.

Simplify $\frac{57 + 33}{5}$ .

Add $57$ and $33$ .

$a = \frac{90}{5}$

$c = 33$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

Divide $90$ by $5$ .

$a = 18$

$c = 33$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$a = 18$

$c = 33$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$a = 18$

$c = 33$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$a = 18$

$c = 33$

$27 = \frac{387 - 4 c}{5}$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

Replace all occurrences of $c$ in $27 = \frac{387 - 4 c}{5}$ with $33$ .

$27 = \frac{387 - 4 \cdot 33}{5}$

$a = 18$

$c = 33$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

Simplify the right side.

Simplify $\frac{387 - 4 \cdot 33}{5}$ .

Simplify the numerator.

Multiply $- 4$ by $33$ .

$27 = \frac{387 - 132}{5}$

$a = 18$

$c = 33$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

Subtract $132$ from $387$ .

$27 = \frac{255}{5}$

$a = 18$

$c = 33$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$27 = \frac{255}{5}$

$a = 18$

$c = 33$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

Divide $255$ by $5$ .

$27 = 51$

$a = 18$

$c = 33$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$27 = 51$

$a = 18$

$c = 33$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$27 = 51$

$a = 18$

$c = 33$

$81 = \frac{3 (248 - c)}{5}$

$b = - \frac{42}{5} - \frac{6 c}{5}$

Replace all occurrences of $c$ in $81 = \frac{3 (248 - c)}{5}$ with $33$ .

$81 = \frac{3 (248 - (33))}{5}$

$27 = 51$

$a = 18$

$c = 33$

$b = - \frac{42}{5} - \frac{6 c}{5}$

Simplify the right side.

Simplify $\frac{3 (248 - (33))}{5}$ .

Simplify the numerator.

Multiply $- 1$ by $33$ .

$81 = \frac{3 (248 - 33)}{5}$

$27 = 51$

$a = 18$

$c = 33$

$b = - \frac{42}{5} - \frac{6 c}{5}$

Subtract $33$ from $248$ .

$81 = \frac{3 \cdot 215}{5}$

$27 = 51$

$a = 18$

$c = 33$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$81 = \frac{3 \cdot 215}{5}$

$27 = 51$

$a = 18$

$c = 33$

$b = - \frac{42}{5} - \frac{6 c}{5}$

Simplify the expression.

Multiply $3$ by $215$ .

$81 = \frac{645}{5}$

$27 = 51$

$a = 18$

$c = 33$

$b = - \frac{42}{5} - \frac{6 c}{5}$

Divide $645$ by $5$ .

$81 = 129$

$27 = 51$

$a = 18$

$c = 33$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$81 = 129$

$27 = 51$

$a = 18$

$c = 33$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$81 = 129$

$27 = 51$

$a = 18$

$c = 33$

$b = - \frac{42}{5} - \frac{6 c}{5}$

$81 = 129$

$27 = 51$

$a = 18$

$c = 33$

$b = - \frac{42}{5} - \frac{6 c}{5}$

Replace all occurrences of $c$ in $b = - \frac{42}{5} - \frac{6 c}{5}$ with $33$ .

$b = - \frac{42}{5} - \frac{6 (33)}{5}$

$81 = 129$

$27 = 51$

$a = 18$

$c = 33$

Simplify the right side.

Simplify $- \frac{42}{5} - \frac{6 (33)}{5}$ .

Combine the numerators over the common denominator.

$b = \frac{- 42 - 6 \cdot 33}{5}$

$81 = 129$

$27 = 51$

$a = 18$

$c = 33$

Simplify the expression.

Multiply $- 6$ by $33$ .

$b = \frac{- 42 - 198}{5}$

$81 = 129$

$27 = 51$

$a = 18$

$c = 33$

Subtract $198$ from $- 42$ .

$b = \frac{- 240}{5}$

$81 = 129$

$27 = 51$

$a = 18$

$c = 33$

Divide $- 240$ by $5$ .

$b = - 48$

$81 = 129$

$27 = 51$

$a = 18$

$c = 33$

$b = - 48$

$81 = 129$

$27 = 51$

$a = 18$

$c = 33$

$b = - 48$

$81 = 129$

$27 = 51$

$a = 18$

$c = 33$

$b = - 48$

$81 = 129$

$27 = 51$

$a = 18$

$c = 33$

$b = - 48$

$81 = 129$

$27 = 51$

$a = 18$

$c = 33$

Since $81 = 129$ 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 $x = 1$ .

Simplify each term.

One to any power is one.

$y = 0 \cdot 1 + (0) \cdot (1) + 0$

Multiply $0$ by $1$ .

$y = 0 + (0) \cdot (1) + 0$

Multiply $0$ by $1$ .

$y = 0 + 0 + 0$

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, $x = 1$ . This check does not pass, since $y = 0$ and $y = 3$ . The function rule can\'t be quadratic.

$0 \neq 3$

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

The function is not quadratic

Step 3

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 $a$ in $3 = a + b + c + d$ .

Rewrite the equation as $a + b + c + d = 3$ .

$a + b + c + d = 3$

$9 = a \cdot 2^{3} + b + c + d$

$27 = a \cdot 3^{3} + b + c + d$

$81 = a \cdot 4^{3} + b + c + d$

$243 = a \cdot 5^{3} + b + c + d$

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

Subtract $b$ from both sides of the equation.

$a + c + d = 3 - b$

$9 = a \cdot 2^{3} + b + c + d$

$27 = a \cdot 3^{3} + b + c + d$

$81 = a \cdot 4^{3} + b + c + d$

$243 = a \cdot 5^{3} + b + c + d$

Subtract $c$ from both sides of the equation.

$a + d = 3 - b - c$

$9 = a \cdot 2^{3} + b + c + d$

$27 = a \cdot 3^{3} + b + c + d$

$81 = a \cdot 4^{3} + b + c + d$

$243 = a \cdot 5^{3} + b + c + d$

Subtract $d$ from both sides of the equation.

$a = 3 - b - c - d$

$9 = a \cdot 2^{3} + b + c + d$

$27 = a \cdot 3^{3} + b + c + d$

$81 = a \cdot 4^{3} + b + c + d$

$243 = a \cdot 5^{3} + b + c + d$

$a = 3 - b - c - d$

$9 = a \cdot 2^{3} + b + c + d$

$27 = a \cdot 3^{3} + b + c + d$

$81 = a \cdot 4^{3} + b + c + d$

$243 = a \cdot 5^{3} + b + c + d$

$a = 3 - b - c - d$

$9 = a \cdot 2^{3} + b + c + d$

$27 = a \cdot 3^{3} + b + c + d$

$81 = a \cdot 4^{3} + b + c + d$

$243 = a \cdot 5^{3} + b + c + d$

Replace all occurrences of $a$ with $3 - b - c - d$ in each equation.

Replace all occurrences of $a$ in $9 = a \cdot 2^{3} + b + c + d$ with $3 - b - c - d$ .

$9 = (3 - b - c - d) \cdot 2^{3} + b + c + d$

$a = 3 - b - c - d$

$27 = a \cdot 3^{3} + b + c + d$

$81 = a \cdot 4^{3} + b + c + d$

$243 = a \cdot 5^{3} + b + c + d$

Simplify the right side.

Simplify $(3 - b - c - d) \cdot 2^{3} + b + c + d$ .

Simplify each term.

Raise $2$ to the power of $3$ .

$9 = (3 - b - c - d) \cdot 8 + b + c + d$

$a = 3 - b - c - d$

$27 = a \cdot 3^{3} + b + c + d$

$81 = a \cdot 4^{3} + b + c + d$

$243 = a \cdot 5^{3} + b + c + d$

Apply the distributive property.

$9 = 3 \cdot 8 - b \cdot 8 - c \cdot 8 - d \cdot 8 + b + c + d$

$a = 3 - b - c - d$

$27 = a \cdot 3^{3} + b + c + d$

$81 = a \cdot 4^{3} + b + c + d$

$243 = a \cdot 5^{3} + b + c + d$

Simplify.

Multiply $3$ by $8$ .

$9 = 24 - b \cdot 8 - c \cdot 8 - d \cdot 8 + b + c + d$

$a = 3 - b - c - d$

$27 = a \cdot 3^{3} + b + c + d$

$81 = a \cdot 4^{3} + b + c + d$

$243 = a \cdot 5^{3} + b + c + d$

Multiply $8$ by $- 1$ .

$9 = 24 - 8 b - c \cdot 8 - d \cdot 8 + b + c + d$

$a = 3 - b - c - d$

$27 = a \cdot 3^{3} + b + c + d$

$81 = a \cdot 4^{3} + b + c + d$

$243 = a \cdot 5^{3} + b + c + d$

Multiply $8$ by $- 1$ .

$9 = 24 - 8 b - 8 c - d \cdot 8 + b + c + d$

$a = 3 - b - c - d$

$27 = a \cdot 3^{3} + b + c + d$

$81 = a \cdot 4^{3} + b + c + d$

$243 = a \cdot 5^{3} + b + c + d$

Multiply $8$ by $- 1$ .

$9 = 24 - 8 b - 8 c - 8 d + b + c + d$

$a = 3 - b - c - d$

$27 = a \cdot 3^{3} + b + c + d$

$81 = a \cdot 4^{3} + b + c + d$

$243 = a \cdot 5^{3} + b + c + d$

$9 = 24 - 8 b - 8 c - 8 d + b + c + d$

$a = 3 - b - c - d$

$27 = a \cdot 3^{3} + b + c + d$

$81 = a \cdot 4^{3} + b + c + d$

$243 = a \cdot 5^{3} + b + c + d$

$9 = 24 - 8 b - 8 c - 8 d + b + c + d$

$a = 3 - b - c - d$

$27 = a \cdot 3^{3} + b + c + d$

$81 = a \cdot 4^{3} + b + c + d$

$243 = a \cdot 5^{3} + b + c + d$

Simplify by adding terms.

Add $- 8 b$ and $b$ .

$9 = 24 - 7 b - 8 c - 8 d + c + d$

$a = 3 - b - c - d$

$27 = a \cdot 3^{3} + b + c + d$

$81 = a \cdot 4^{3} + b + c + d$

$243 = a \cdot 5^{3} + b + c + d$

Add $- 8 c$ and $c$ .

$9 = 24 - 7 b - 7 c - 8 d + d$

$a = 3 - b - c - d$

$27 = a \cdot 3^{3} + b + c + d$

$81 = a \cdot 4^{3} + b + c + d$

$243 = a \cdot 5^{3} + b + c + d$

Add $- 8 d$ and $d$ .

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$27 = a \cdot 3^{3} + b + c + d$

$81 = a \cdot 4^{3} + b + c + d$

$243 = a \cdot 5^{3} + b + c + d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$27 = a \cdot 3^{3} + b + c + d$

$81 = a \cdot 4^{3} + b + c + d$

$243 = a \cdot 5^{3} + b + c + d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$27 = a \cdot 3^{3} + b + c + d$

$81 = a \cdot 4^{3} + b + c + d$

$243 = a \cdot 5^{3} + b + c + d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$27 = a \cdot 3^{3} + b + c + d$

$81 = a \cdot 4^{3} + b + c + d$

$243 = a \cdot 5^{3} + b + c + d$

Replace all occurrences of $a$ in $27 = a \cdot 3^{3} + b + c + d$ with $3 - b - c - d$ .

$27 = (3 - b - c - d) \cdot 3^{3} + b + c + d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$81 = a \cdot 4^{3} + b + c + d$

$243 = a \cdot 5^{3} + b + c + d$

Simplify the right side.

Simplify $(3 - b - c - d) \cdot 3^{3} + b + c + d$ .

Simplify each term.

Raise $3$ to the power of $3$ .

$27 = (3 - b - c - d) \cdot 27 + b + c + d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$81 = a \cdot 4^{3} + b + c + d$

$243 = a \cdot 5^{3} + b + c + d$

Apply the distributive property.

$27 = 3 \cdot 27 - b \cdot 27 - c \cdot 27 - d \cdot 27 + b + c + d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$81 = a \cdot 4^{3} + b + c + d$

$243 = a \cdot 5^{3} + b + c + d$

Simplify.

Multiply $3$ by $27$ .

$27 = 81 - b \cdot 27 - c \cdot 27 - d \cdot 27 + b + c + d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$81 = a \cdot 4^{3} + b + c + d$

$243 = a \cdot 5^{3} + b + c + d$

Multiply $27$ by $- 1$ .

$27 = 81 - 27 b - c \cdot 27 - d \cdot 27 + b + c + d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$81 = a \cdot 4^{3} + b + c + d$

$243 = a \cdot 5^{3} + b + c + d$

Multiply $27$ by $- 1$ .

$27 = 81 - 27 b - 27 c - d \cdot 27 + b + c + d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$81 = a \cdot 4^{3} + b + c + d$

$243 = a \cdot 5^{3} + b + c + d$

Multiply $27$ by $- 1$ .

$27 = 81 - 27 b - 27 c - 27 d + b + c + d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$81 = a \cdot 4^{3} + b + c + d$

$243 = a \cdot 5^{3} + b + c + d$

$27 = 81 - 27 b - 27 c - 27 d + b + c + d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$81 = a \cdot 4^{3} + b + c + d$

$243 = a \cdot 5^{3} + b + c + d$

$27 = 81 - 27 b - 27 c - 27 d + b + c + d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$81 = a \cdot 4^{3} + b + c + d$

$243 = a \cdot 5^{3} + b + c + d$

Simplify by adding terms.

Add $- 27 b$ and $b$ .

$27 = 81 - 26 b - 27 c - 27 d + c + d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$81 = a \cdot 4^{3} + b + c + d$

$243 = a \cdot 5^{3} + b + c + d$

Add $- 27 c$ and $c$ .

$27 = 81 - 26 b - 26 c - 27 d + d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$81 = a \cdot 4^{3} + b + c + d$

$243 = a \cdot 5^{3} + b + c + d$

Add $- 27 d$ and $d$ .

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$81 = a \cdot 4^{3} + b + c + d$

$243 = a \cdot 5^{3} + b + c + d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$81 = a \cdot 4^{3} + b + c + d$

$243 = a \cdot 5^{3} + b + c + d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$81 = a \cdot 4^{3} + b + c + d$

$243 = a \cdot 5^{3} + b + c + d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$81 = a \cdot 4^{3} + b + c + d$

$243 = a \cdot 5^{3} + b + c + d$

Replace all occurrences of $a$ in $81 = a \cdot 4^{3} + b + c + d$ with $3 - b - c - d$ .

$81 = (3 - b - c - d) \cdot 4^{3} + b + c + d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$243 = a \cdot 5^{3} + b + c + d$

Simplify the right side.

Simplify $(3 - b - c - d) \cdot 4^{3} + b + c + d$ .

Simplify each term.

Raise $4$ to the power of $3$ .

$81 = (3 - b - c - d) \cdot 64 + b + c + d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$243 = a \cdot 5^{3} + b + c + d$

Apply the distributive property.

$81 = 3 \cdot 64 - b \cdot 64 - c \cdot 64 - d \cdot 64 + b + c + d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$243 = a \cdot 5^{3} + b + c + d$

Simplify.

Multiply $3$ by $64$ .

$81 = 192 - b \cdot 64 - c \cdot 64 - d \cdot 64 + b + c + d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$243 = a \cdot 5^{3} + b + c + d$

Multiply $64$ by $- 1$ .

$81 = 192 - 64 b - c \cdot 64 - d \cdot 64 + b + c + d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$243 = a \cdot 5^{3} + b + c + d$

Multiply $64$ by $- 1$ .

$81 = 192 - 64 b - 64 c - d \cdot 64 + b + c + d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$243 = a \cdot 5^{3} + b + c + d$

Multiply $64$ by $- 1$ .

$81 = 192 - 64 b - 64 c - 64 d + b + c + d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$243 = a \cdot 5^{3} + b + c + d$

$81 = 192 - 64 b - 64 c - 64 d + b + c + d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$243 = a \cdot 5^{3} + b + c + d$

$81 = 192 - 64 b - 64 c - 64 d + b + c + d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$243 = a \cdot 5^{3} + b + c + d$

Simplify by adding terms.

Add $- 64 b$ and $b$ .

$81 = 192 - 63 b - 64 c - 64 d + c + d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$243 = a \cdot 5^{3} + b + c + d$

Add $- 64 c$ and $c$ .

$81 = 192 - 63 b - 63 c - 64 d + d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$243 = a \cdot 5^{3} + b + c + d$

Add $- 64 d$ and $d$ .

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$243 = a \cdot 5^{3} + b + c + d$

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$243 = a \cdot 5^{3} + b + c + d$

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$243 = a \cdot 5^{3} + b + c + d$

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$243 = a \cdot 5^{3} + b + c + d$

Replace all occurrences of $a$ in $243 = a \cdot 5^{3} + b + c + d$ with $3 - b - c - d$ .

$243 = (3 - b - c - d) \cdot 5^{3} + b + c + d$

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Simplify the right side.

Simplify $(3 - b - c - d) \cdot 5^{3} + b + c + d$ .

Simplify each term.

Raise $5$ to the power of $3$ .

$243 = (3 - b - c - d) \cdot 125 + b + c + d$

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Apply the distributive property.

$243 = 3 \cdot 125 - b \cdot 125 - c \cdot 125 - d \cdot 125 + b + c + d$

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Simplify.

Multiply $3$ by $125$ .

$243 = 375 - b \cdot 125 - c \cdot 125 - d \cdot 125 + b + c + d$

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Multiply $125$ by $- 1$ .

$243 = 375 - 125 b - c \cdot 125 - d \cdot 125 + b + c + d$

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Multiply $125$ by $- 1$ .

$243 = 375 - 125 b - 125 c - d \cdot 125 + b + c + d$

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Multiply $125$ by $- 1$ .

$243 = 375 - 125 b - 125 c - 125 d + b + c + d$

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$243 = 375 - 125 b - 125 c - 125 d + b + c + d$

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$243 = 375 - 125 b - 125 c - 125 d + b + c + d$

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Simplify by adding terms.

Add $- 125 b$ and $b$ .

$243 = 375 - 124 b - 125 c - 125 d + c + d$

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Add $- 125 c$ and $c$ .

$243 = 375 - 124 b - 124 c - 125 d + d$

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Add $- 125 d$ and $d$ .

$243 = 375 - 124 b - 124 c - 124 d$

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$243 = 375 - 124 b - 124 c - 124 d$

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$243 = 375 - 124 b - 124 c - 124 d$

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$243 = 375 - 124 b - 124 c - 124 d$

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$243 = 375 - 124 b - 124 c - 124 d$

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Solve for $b$ in $243 = 375 - 124 b - 124 c - 124 d$ .

Rewrite the equation as $375 - 124 b - 124 c - 124 d = 243$ .

$375 - 124 b - 124 c - 124 d = 243$

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

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

Subtract $375$ from both sides of the equation.

$- 124 b - 124 c - 124 d = 243 - 375$

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Add $124 c$ to both sides of the equation.

$- 124 b - 124 d = 243 - 375 + 124 c$

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Add $124 d$ to both sides of the equation.

$- 124 b = 243 - 375 + 124 c + 124 d$

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Subtract $375$ from $243$ .

$- 124 b = - 132 + 124 c + 124 d$

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$- 124 b = - 132 + 124 c + 124 d$

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Divide each term in $- 124 b = - 132 + 124 c + 124 d$ by $- 124$ and simplify.

Divide each term in $- 124 b = - 132 + 124 c + 124 d$ by $- 124$ .

$\frac{- 124 b}{- 124} = \frac{- 132}{- 124} + \frac{124 c}{- 124} + \frac{124 d}{- 124}$

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Simplify the left side.

Cancel the common factor of $- 124$ .

Cancel the common factor.

$\frac{- 124 b}{- 124} = \frac{- 132}{- 124} + \frac{124 c}{- 124} + \frac{124 d}{- 124}$

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Divide $b$ by $1$ .

$b = \frac{- 132}{- 124} + \frac{124 c}{- 124} + \frac{124 d}{- 124}$

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$b = \frac{- 132}{- 124} + \frac{124 c}{- 124} + \frac{124 d}{- 124}$

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$b = \frac{- 132}{- 124} + \frac{124 c}{- 124} + \frac{124 d}{- 124}$

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Simplify the right side.

Simplify each term.

Cancel the common factor of $- 132$ and $- 124$ .

Factor $- 4$ out of $- 132$ .

$b = \frac{- 4 \cdot 33}{- 124} + \frac{124 c}{- 124} + \frac{124 d}{- 124}$

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Cancel the common factors.

Factor $- 4$ out of $- 124$ .

$b = \frac{- 4 \cdot 33}{- 4 \cdot 31} + \frac{124 c}{- 124} + \frac{124 d}{- 124}$

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Cancel the common factor.

$b = \frac{- 4 \cdot 33}{- 4 \cdot 31} + \frac{124 c}{- 124} + \frac{124 d}{- 124}$

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Rewrite the expression.

$b = \frac{33}{31} + \frac{124 c}{- 124} + \frac{124 d}{- 124}$

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$b = \frac{33}{31} + \frac{124 c}{- 124} + \frac{124 d}{- 124}$

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$b = \frac{33}{31} + \frac{124 c}{- 124} + \frac{124 d}{- 124}$

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Cancel the common factor of $124$ and $- 124$ .

Factor $124$ out of $124 c$ .

$b = \frac{33}{31} + \frac{124 (c)}{- 124} + \frac{124 d}{- 124}$

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Move the negative one from the denominator of $\frac{c}{- 1}$ .

$b = \frac{33}{31} - 1 \cdot c + \frac{124 d}{- 124}$

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$b = \frac{33}{31} - 1 \cdot c + \frac{124 d}{- 124}$

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Rewrite $- 1 \cdot c$ as $- c$ .

$b = \frac{33}{31} - c + \frac{124 d}{- 124}$

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Cancel the common factor of $124$ and $- 124$ .

Factor $124$ out of $124 d$ .

$b = \frac{33}{31} - c + \frac{124 (d)}{- 124}$

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Move the negative one from the denominator of $\frac{d}{- 1}$ .

$b = \frac{33}{31} - c - 1 \cdot d$

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$b = \frac{33}{31} - c - 1 \cdot d$

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Rewrite $- 1 \cdot d$ as $- d$ .

$b = \frac{33}{31} - c - d$

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$b = \frac{33}{31} - c - d$

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$b = \frac{33}{31} - c - d$

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$b = \frac{33}{31} - c - d$

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$b = \frac{33}{31} - c - d$

$81 = 192 - 63 b - 63 c - 63 d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Replace all occurrences of $b$ with $\frac{33}{31} - c - d$ in each equation.

Replace all occurrences of $b$ in $81 = 192 - 63 b - 63 c - 63 d$ with $\frac{33}{31} - c - d$ .

$81 = 192 - 63 (\frac{33}{31} - c - d) - 63 c - 63 d$

$b = \frac{33}{31} - c - d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Simplify the right side.

Simplify $192 - 63 (\frac{33}{31} - c - d) - 63 c - 63 d$ .

Simplify each term.

Apply the distributive property.

$81 = 192 - 63 (\frac{33}{31}) - 63 (- c) - 63 (- d) - 63 c - 63 d$

$b = \frac{33}{31} - c - d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Simplify.

Multiply $- 63 (\frac{33}{31})$ .

Combine $- 63$ and $\frac{33}{31}$ .

$81 = 192 + \frac{- 63 \cdot 33}{31} - 63 (- c) - 63 (- d) - 63 c - 63 d$

$b = \frac{33}{31} - c - d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Multiply $- 63$ by $33$ .

$81 = 192 + \frac{- 2079}{31} - 63 (- c) - 63 (- d) - 63 c - 63 d$

$b = \frac{33}{31} - c - d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$81 = 192 + \frac{- 2079}{31} - 63 (- c) - 63 (- d) - 63 c - 63 d$

$b = \frac{33}{31} - c - d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Multiply $- 1$ by $- 63$ .

$81 = 192 + \frac{- 2079}{31} + 63 c - 63 (- d) - 63 c - 63 d$

$b = \frac{33}{31} - c - d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Multiply $- 1$ by $- 63$ .

$81 = 192 + \frac{- 2079}{31} + 63 c + 63 d - 63 c - 63 d$

$b = \frac{33}{31} - c - d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$81 = 192 + \frac{- 2079}{31} + 63 c + 63 d - 63 c - 63 d$

$b = \frac{33}{31} - c - d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Move the negative in front of the fraction.

$81 = 192 - \frac{2079}{31} + 63 c + 63 d - 63 c - 63 d$

$b = \frac{33}{31} - c - d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$81 = 192 - \frac{2079}{31} + 63 c + 63 d - 63 c - 63 d$

$b = \frac{33}{31} - c - d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Combine the opposite terms in $192 - \frac{2079}{31} + 63 c + 63 d - 63 c - 63 d$ .

Subtract $63 c$ from $63 c$ .

$81 = 192 - \frac{2079}{31} + 63 d + 0 - 63 d$

$b = \frac{33}{31} - c - d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Add $192 - \frac{2079}{31} + 63 d$ and $0$ .

$81 = 192 - \frac{2079}{31} + 63 d - 63 d$

$b = \frac{33}{31} - c - d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Subtract $63 d$ from $63 d$ .

$81 = 192 - \frac{2079}{31} + 0$

$b = \frac{33}{31} - c - d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Add $192 - \frac{2079}{31}$ and $0$ .

$81 = 192 - \frac{2079}{31}$

$b = \frac{33}{31} - c - d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$81 = 192 - \frac{2079}{31}$

$b = \frac{33}{31} - c - d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

To write $192$ as a fraction with a common denominator, multiply by $\frac{31}{31}$ .

$81 = 192 \cdot \frac{31}{31} - \frac{2079}{31}$

$b = \frac{33}{31} - c - d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Combine $192$ and $\frac{31}{31}$ .

$81 = \frac{192 \cdot 31}{31} - \frac{2079}{31}$

$b = \frac{33}{31} - c - d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Combine the numerators over the common denominator.

$81 = \frac{192 \cdot 31 - 2079}{31}$

$b = \frac{33}{31} - c - d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Simplify the numerator.

Multiply $192$ by $31$ .

$81 = \frac{5952 - 2079}{31}$

$b = \frac{33}{31} - c - d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Subtract $2079$ from $5952$ .

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$27 = 81 - 26 b - 26 c - 26 d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Replace all occurrences of $b$ in $27 = 81 - 26 b - 26 c - 26 d$ with $\frac{33}{31} - c - d$ .

$27 = 81 - 26 (\frac{33}{31} - c - d) - 26 c - 26 d$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Simplify the right side.

Simplify $81 - 26 (\frac{33}{31} - c - d) - 26 c - 26 d$ .

Simplify each term.

Apply the distributive property.

$27 = 81 - 26 (\frac{33}{31}) - 26 (- c) - 26 (- d) - 26 c - 26 d$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Simplify.

Multiply $- 26 (\frac{33}{31})$ .

Combine $- 26$ and $\frac{33}{31}$ .

$27 = 81 + \frac{- 26 \cdot 33}{31} - 26 (- c) - 26 (- d) - 26 c - 26 d$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Multiply $- 26$ by $33$ .

$27 = 81 + \frac{- 858}{31} - 26 (- c) - 26 (- d) - 26 c - 26 d$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$27 = 81 + \frac{- 858}{31} - 26 (- c) - 26 (- d) - 26 c - 26 d$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Multiply $- 1$ by $- 26$ .

$27 = 81 + \frac{- 858}{31} + 26 c - 26 (- d) - 26 c - 26 d$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Multiply $- 1$ by $- 26$ .

$27 = 81 + \frac{- 858}{31} + 26 c + 26 d - 26 c - 26 d$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$27 = 81 + \frac{- 858}{31} + 26 c + 26 d - 26 c - 26 d$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Move the negative in front of the fraction.

$27 = 81 - \frac{858}{31} + 26 c + 26 d - 26 c - 26 d$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$27 = 81 - \frac{858}{31} + 26 c + 26 d - 26 c - 26 d$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Combine the opposite terms in $81 - \frac{858}{31} + 26 c + 26 d - 26 c - 26 d$ .

Subtract $26 c$ from $26 c$ .

$27 = 81 - \frac{858}{31} + 26 d + 0 - 26 d$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Add $81 - \frac{858}{31} + 26 d$ and $0$ .

$27 = 81 - \frac{858}{31} + 26 d - 26 d$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Subtract $26 d$ from $26 d$ .

$27 = 81 - \frac{858}{31} + 0$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Add $81 - \frac{858}{31}$ and $0$ .

$27 = 81 - \frac{858}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$27 = 81 - \frac{858}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

To write $81$ as a fraction with a common denominator, multiply by $\frac{31}{31}$ .

$27 = 81 \cdot \frac{31}{31} - \frac{858}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Combine $81$ and $\frac{31}{31}$ .

$27 = \frac{81 \cdot 31}{31} - \frac{858}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Combine the numerators over the common denominator.

$27 = \frac{81 \cdot 31 - 858}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Simplify the numerator.

Multiply $81$ by $31$ .

$27 = \frac{2511 - 858}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Subtract $858$ from $2511$ .

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$9 = 24 - 7 b - 7 c - 7 d$

$a = 3 - b - c - d$

Replace all occurrences of $b$ in $9 = 24 - 7 b - 7 c - 7 d$ with $\frac{33}{31} - c - d$ .

$9 = 24 - 7 (\frac{33}{31} - c - d) - 7 c - 7 d$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$a = 3 - b - c - d$

Simplify the right side.

Simplify $24 - 7 (\frac{33}{31} - c - d) - 7 c - 7 d$ .

Simplify each term.

Apply the distributive property.

$9 = 24 - 7 (\frac{33}{31}) - 7 (- c) - 7 (- d) - 7 c - 7 d$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$a = 3 - b - c - d$

Simplify.

Multiply $- 7 (\frac{33}{31})$ .

Combine $- 7$ and $\frac{33}{31}$ .

$9 = 24 + \frac{- 7 \cdot 33}{31} - 7 (- c) - 7 (- d) - 7 c - 7 d$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$a = 3 - b - c - d$

Multiply $- 7$ by $33$ .

$9 = 24 + \frac{- 231}{31} - 7 (- c) - 7 (- d) - 7 c - 7 d$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$a = 3 - b - c - d$

$9 = 24 + \frac{- 231}{31} - 7 (- c) - 7 (- d) - 7 c - 7 d$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$a = 3 - b - c - d$

Multiply $- 1$ by $- 7$ .

$9 = 24 + \frac{- 231}{31} + 7 c - 7 (- d) - 7 c - 7 d$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$a = 3 - b - c - d$

Multiply $- 1$ by $- 7$ .

$9 = 24 + \frac{- 231}{31} + 7 c + 7 d - 7 c - 7 d$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$a = 3 - b - c - d$

$9 = 24 + \frac{- 231}{31} + 7 c + 7 d - 7 c - 7 d$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$a = 3 - b - c - d$

Move the negative in front of the fraction.

$9 = 24 - \frac{231}{31} + 7 c + 7 d - 7 c - 7 d$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$a = 3 - b - c - d$

$9 = 24 - \frac{231}{31} + 7 c + 7 d - 7 c - 7 d$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$a = 3 - b - c - d$

Combine the opposite terms in $24 - \frac{231}{31} + 7 c + 7 d - 7 c - 7 d$ .

Subtract $7 c$ from $7 c$ .

$9 = 24 - \frac{231}{31} + 7 d + 0 - 7 d$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$a = 3 - b - c - d$

Add $24 - \frac{231}{31} + 7 d$ and $0$ .

$9 = 24 - \frac{231}{31} + 7 d - 7 d$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$a = 3 - b - c - d$

Subtract $7 d$ from $7 d$ .

$9 = 24 - \frac{231}{31} + 0$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$a = 3 - b - c - d$

Add $24 - \frac{231}{31}$ and $0$ .

$9 = 24 - \frac{231}{31}$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$a = 3 - b - c - d$

$9 = 24 - \frac{231}{31}$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$a = 3 - b - c - d$

To write $24$ as a fraction with a common denominator, multiply by $\frac{31}{31}$ .

$9 = 24 \cdot \frac{31}{31} - \frac{231}{31}$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$a = 3 - b - c - d$

Combine $24$ and $\frac{31}{31}$ .

$9 = \frac{24 \cdot 31}{31} - \frac{231}{31}$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$a = 3 - b - c - d$

Combine the numerators over the common denominator.

$9 = \frac{24 \cdot 31 - 231}{31}$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$a = 3 - b - c - d$

Simplify the numerator.

Multiply $24$ by $31$ .

$9 = \frac{744 - 231}{31}$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$a = 3 - b - c - d$

Subtract $231$ from $744$ .

$9 = \frac{513}{31}$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$a = 3 - b - c - d$

$9 = \frac{513}{31}$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$a = 3 - b - c - d$

$9 = \frac{513}{31}$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$a = 3 - b - c - d$

$9 = \frac{513}{31}$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$a = 3 - b - c - d$

Replace all occurrences of $b$ in $a = 3 - b - c - d$ with $\frac{33}{31} - c - d$ .

$a = 3 - (\frac{33}{31} - c - d) - c - d$

$9 = \frac{513}{31}$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

Simplify the right side.

Simplify $3 - (\frac{33}{31} - c - d) - c - d$ .

Simplify each term.

Apply the distributive property.

$a = 3 - \frac{33}{31} + c + d - c - d$

$9 = \frac{513}{31}$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

Simplify.

Multiply $- - c$ .

Multiply $- 1$ by $- 1$ .

$a = 3 - \frac{33}{31} + 1 c + d - c - d$

$9 = \frac{513}{31}$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

Multiply $c$ by $1$ .

$a = 3 - \frac{33}{31} + c + d - c - d$

$9 = \frac{513}{31}$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$a = 3 - \frac{33}{31} + c + d - c - d$

$9 = \frac{513}{31}$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

Multiply $- - d$ .

Multiply $- 1$ by $- 1$ .

$a = 3 - \frac{33}{31} + c + 1 d - c - d$

$9 = \frac{513}{31}$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

Multiply $d$ by $1$ .

$a = 3 - \frac{33}{31} + c + d - c - d$

$9 = \frac{513}{31}$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$a = 3 - \frac{33}{31} + c + d - c - d$

$9 = \frac{513}{31}$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$a = 3 - \frac{33}{31} + c + d - c - d$

$9 = \frac{513}{31}$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$a = 3 - \frac{33}{31} + c + d - c - d$

$9 = \frac{513}{31}$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

Combine the opposite terms in $3 - \frac{33}{31} + c + d - c - d$ .

Subtract $c$ from $c$ .

$a = 3 - \frac{33}{31} + d + 0 - d$

$9 = \frac{513}{31}$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

Add $3 - \frac{33}{31} + d$ and $0$ .

$a = 3 - \frac{33}{31} + d - d$

$9 = \frac{513}{31}$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

Subtract $d$ from $d$ .

$a = 3 - \frac{33}{31} + 0$

$9 = \frac{513}{31}$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

Add $3 - \frac{33}{31}$ and $0$ .

$a = 3 - \frac{33}{31}$

$9 = \frac{513}{31}$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$a = 3 - \frac{33}{31}$

$9 = \frac{513}{31}$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

To write $3$ as a fraction with a common denominator, multiply by $\frac{31}{31}$ .

$a = 3 \cdot \frac{31}{31} - \frac{33}{31}$

$9 = \frac{513}{31}$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

Combine $3$ and $\frac{31}{31}$ .

$a = \frac{3 \cdot 31}{31} - \frac{33}{31}$

$9 = \frac{513}{31}$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

Combine the numerators over the common denominator.

$a = \frac{3 \cdot 31 - 33}{31}$

$9 = \frac{513}{31}$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

Simplify the numerator.

Multiply $3$ by $31$ .

$a = \frac{93 - 33}{31}$

$9 = \frac{513}{31}$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

Subtract $33$ from $93$ .

$a = \frac{60}{31}$

$9 = \frac{513}{31}$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$a = \frac{60}{31}$

$9 = \frac{513}{31}$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$a = \frac{60}{31}$

$9 = \frac{513}{31}$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$a = \frac{60}{31}$

$9 = \frac{513}{31}$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

$a = \frac{60}{31}$

$9 = \frac{513}{31}$

$27 = \frac{1653}{31}$

$81 = \frac{3873}{31}$

$b = \frac{33}{31} - c - d$

Since $9 = \frac{513}{31}$ 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 $x = 1$ .

Simplify each term.

One to any power is one.

$y = 0 \cdot 1 + (0) \cdot (1^{2}) + (0) \cdot ((1) \cdot 0)$

Multiply $0$ by $1$ .

$y = 0 + (0) \cdot (1^{2}) + (0) \cdot ((1) \cdot 0)$

One to any power is one.

$y = 0 + 0 \cdot 1 + (0) \cdot ((1) \cdot 0)$

Multiply $0$ by $1$ .

$y = 0 + 0 + (0) \cdot ((1) \cdot 0)$

Multiply $(0) ((1) \cdot 0)$ .

Multiply $0$ by $1$ .

$y = 0 + 0 + 0 \cdot 0$

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, $x = 1$ . This check does not pass, since $y = 0$ and $y = 3$ . The function rule can\'t be cubic.

$0 \neq 3$

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

The function is not cubic

Step 4

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],[1,3],[2,9],[3,27],[4,81],[5,243]]

Related Questions

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