Solve the Matrix Equation [[x+9,-2,-9y],[8,-2x,-7],[1,y-5,6]]=[[10x+0,-2,-36],[8,-2,-7],[1,-1,6]]

$[\begin{array}{c} x + 9 & - 2 & - 9 y \\ 8 & - 2 x & - 7 \\ 1 & y - 5 & 6 \end{array}] = [\begin{array}{c} 10 x + 0 & - 2 & - 36 \\ 8 & - 2 & - 7 \\ 1 & - 1 & 6 \end{array}]$

Rearrange $10 x + 0$ .

$[\begin{array}{c} x + 9 & - 2 & - 9 y \\ 8 & - 2 x & - 7 \\ 1 & y - 5 & 6 \end{array}] = [\begin{array}{c} 10 x & - 2 & - 36 \\ 8 & - 2 & - 7 \\ 1 & - 1 & 6 \end{array}]$

Find the function rule.

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 $y = a x + b$ .

$- 2 = a (- 2) + b 8 = a (8) + b - 7 = a (- 7) + b 1 = a (1) + b 6 = a (6) + b$

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

Solve for $a$ in $1 = a + b$ .

Rewrite the equation as $a + b = 1$ .

$a + b = 1$

$- 2 = a (- 2) + b$

$8 = a (8) + b$

$- 7 = a (- 7) + b$

$6 = a (6) + b$

Subtract $b$ from both sides of the equation.

$a = 1 - b$

$- 2 = a (- 2) + b$

$8 = a (8) + b$

$- 7 = a (- 7) + b$

$6 = a (6) + b$

$a = 1 - b$

$- 2 = a (- 2) + b$

$8 = a (8) + b$

$- 7 = a (- 7) + b$

$6 = a (6) + b$

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

Replace all occurrences of $a$ in $- 2 = a (- 2) + b$ with $1 - b$ .

$- 2 = (1 - b) (- 2) + b$

$a = 1 - b$

$8 = a (8) + b$

$- 7 = a (- 7) + b$

$6 = a (6) + b$

Simplify the right side.

Simplify $(1 - b) (- 2) + b$ .

Simplify each term.

Apply the distributive property.

$- 2 = 1 \cdot - 2 - b \cdot - 2 + b$

$a = 1 - b$

$8 = a (8) + b$

$- 7 = a (- 7) + b$

$6 = a (6) + b$

Multiply $- 2$ by $1$ .

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

$a = 1 - b$

$8 = a (8) + b$

$- 7 = a (- 7) + b$

$6 = a (6) + b$

Multiply $- 2$ by $- 1$ .

$- 2 = - 2 + 2 b + b$

$a = 1 - b$

$8 = a (8) + b$

$- 7 = a (- 7) + b$

$6 = a (6) + b$

$- 2 = - 2 + 2 b + b$

$a = 1 - b$

$8 = a (8) + b$

$- 7 = a (- 7) + b$

$6 = a (6) + b$

Add $2 b$ and $b$ .

$- 2 = - 2 + 3 b$

$a = 1 - b$

$8 = a (8) + b$

$- 7 = a (- 7) + b$

$6 = a (6) + b$

$- 2 = - 2 + 3 b$

$a = 1 - b$

$8 = a (8) + b$

$- 7 = a (- 7) + b$

$6 = a (6) + b$

$- 2 = - 2 + 3 b$

$a = 1 - b$

$8 = a (8) + b$

$- 7 = a (- 7) + b$

$6 = a (6) + b$

Replace all occurrences of $a$ in $8 = a (8) + b$ with $1 - b$ .

$8 = (1 - b) (8) + b$

$- 2 = - 2 + 3 b$

$a = 1 - b$

$- 7 = a (- 7) + b$

$6 = a (6) + b$

Simplify the right side.

Simplify $(1 - b) (8) + b$ .

Simplify each term.

Apply the distributive property.

$8 = 1 \cdot 8 - b \cdot 8 + b$

$- 2 = - 2 + 3 b$

$a = 1 - b$

$- 7 = a (- 7) + b$

$6 = a (6) + b$

Multiply $8$ by $1$ .

$8 = 8 - b \cdot 8 + b$

$- 2 = - 2 + 3 b$

$a = 1 - b$

$- 7 = a (- 7) + b$

$6 = a (6) + b$

Multiply $8$ by $- 1$ .

$8 = 8 - 8 b + b$

$- 2 = - 2 + 3 b$

$a = 1 - b$

$- 7 = a (- 7) + b$

$6 = a (6) + b$

$8 = 8 - 8 b + b$

$- 2 = - 2 + 3 b$

$a = 1 - b$

$- 7 = a (- 7) + b$

$6 = a (6) + b$

Add $- 8 b$ and $b$ .

$8 = 8 - 7 b$

$- 2 = - 2 + 3 b$

$a = 1 - b$

$- 7 = a (- 7) + b$

$6 = a (6) + b$

$8 = 8 - 7 b$

$- 2 = - 2 + 3 b$

$a = 1 - b$

$- 7 = a (- 7) + b$

$6 = a (6) + b$

$8 = 8 - 7 b$

$- 2 = - 2 + 3 b$

$a = 1 - b$

$- 7 = a (- 7) + b$

$6 = a (6) + b$

Replace all occurrences of $a$ in $- 7 = a (- 7) + b$ with $1 - b$ .

$- 7 = (1 - b) (- 7) + b$

$8 = 8 - 7 b$

$- 2 = - 2 + 3 b$

$a = 1 - b$

$6 = a (6) + b$

Simplify the right side.

Simplify $(1 - b) (- 7) + b$ .

Simplify each term.

Apply the distributive property.

$- 7 = 1 \cdot - 7 - b \cdot - 7 + b$

$8 = 8 - 7 b$

$- 2 = - 2 + 3 b$

$a = 1 - b$

$6 = a (6) + b$

Multiply $- 7$ by $1$ .

$- 7 = - 7 - b \cdot - 7 + b$

$8 = 8 - 7 b$

$- 2 = - 2 + 3 b$

$a = 1 - b$

$6 = a (6) + b$

Multiply $- 7$ by $- 1$ .

$- 7 = - 7 + 7 b + b$

$8 = 8 - 7 b$

$- 2 = - 2 + 3 b$

$a = 1 - b$

$6 = a (6) + b$

$- 7 = - 7 + 7 b + b$

$8 = 8 - 7 b$

$- 2 = - 2 + 3 b$

$a = 1 - b$

$6 = a (6) + b$

Add $7 b$ and $b$ .

$- 7 = - 7 + 8 b$

$8 = 8 - 7 b$

$- 2 = - 2 + 3 b$

$a = 1 - b$

$6 = a (6) + b$

$- 7 = - 7 + 8 b$

$8 = 8 - 7 b$

$- 2 = - 2 + 3 b$

$a = 1 - b$

$6 = a (6) + b$

$- 7 = - 7 + 8 b$

$8 = 8 - 7 b$

$- 2 = - 2 + 3 b$

$a = 1 - b$

$6 = a (6) + b$

Replace all occurrences of $a$ in $6 = a (6) + b$ with $1 - b$ .

$6 = (1 - b) (6) + b$

$- 7 = - 7 + 8 b$

$8 = 8 - 7 b$

$- 2 = - 2 + 3 b$

$a = 1 - b$

Simplify the right side.

Simplify $(1 - b) (6) + b$ .

Simplify each term.

Apply the distributive property.

$6 = 1 \cdot 6 - b \cdot 6 + b$

$- 7 = - 7 + 8 b$

$8 = 8 - 7 b$

$- 2 = - 2 + 3 b$

$a = 1 - b$

Multiply $6$ by $1$ .

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

$- 7 = - 7 + 8 b$

$8 = 8 - 7 b$

$- 2 = - 2 + 3 b$

$a = 1 - b$

Multiply $6$ by $- 1$ .

$6 = 6 - 6 b + b$

$- 7 = - 7 + 8 b$

$8 = 8 - 7 b$

$- 2 = - 2 + 3 b$

$a = 1 - b$

$6 = 6 - 6 b + b$

$- 7 = - 7 + 8 b$

$8 = 8 - 7 b$

$- 2 = - 2 + 3 b$

$a = 1 - b$

Add $- 6 b$ and $b$ .

$6 = 6 - 5 b$

$- 7 = - 7 + 8 b$

$8 = 8 - 7 b$

$- 2 = - 2 + 3 b$

$a = 1 - b$

$6 = 6 - 5 b$

$- 7 = - 7 + 8 b$

$8 = 8 - 7 b$

$- 2 = - 2 + 3 b$

$a = 1 - b$

$6 = 6 - 5 b$

$- 7 = - 7 + 8 b$

$8 = 8 - 7 b$

$- 2 = - 2 + 3 b$

$a = 1 - b$

$6 = 6 - 5 b$

$- 7 = - 7 + 8 b$

$8 = 8 - 7 b$

$- 2 = - 2 + 3 b$

$a = 1 - b$

Solve for $b$ in $6 = 6 - 5 b$ .

Rewrite the equation as $6 - 5 b = 6$ .

$6 - 5 b = 6$

$- 7 = - 7 + 8 b$

$8 = 8 - 7 b$

$- 2 = - 2 + 3 b$

$a = 1 - b$

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

Subtract $6$ from both sides of the equation.

$- 5 b = 6 - 6$

$- 7 = - 7 + 8 b$

$8 = 8 - 7 b$

$- 2 = - 2 + 3 b$

$a = 1 - b$

Subtract $6$ from $6$ .

$- 5 b = 0$

$- 7 = - 7 + 8 b$

$8 = 8 - 7 b$

$- 2 = - 2 + 3 b$

$a = 1 - b$

$- 5 b = 0$

$- 7 = - 7 + 8 b$

$8 = 8 - 7 b$

$- 2 = - 2 + 3 b$

$a = 1 - b$

Divide each term in $- 5 b = 0$ by $- 5$ and simplify.

Divide each term in $- 5 b = 0$ by $- 5$ .

$\frac{- 5 b}{- 5} = \frac{0}{- 5}$

$- 7 = - 7 + 8 b$

$8 = 8 - 7 b$

$- 2 = - 2 + 3 b$

$a = 1 - b$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 b}{- 5} = \frac{0}{- 5}$

$- 7 = - 7 + 8 b$

$8 = 8 - 7 b$

$- 2 = - 2 + 3 b$

$a = 1 - b$

Divide $b$ by $1$ .

$b = \frac{0}{- 5}$

$- 7 = - 7 + 8 b$

$8 = 8 - 7 b$

$- 2 = - 2 + 3 b$

$a = 1 - b$

$b = \frac{0}{- 5}$

$- 7 = - 7 + 8 b$

$8 = 8 - 7 b$

$- 2 = - 2 + 3 b$

$a = 1 - b$

$b = \frac{0}{- 5}$

$- 7 = - 7 + 8 b$

$8 = 8 - 7 b$

$- 2 = - 2 + 3 b$

$a = 1 - b$

Simplify the right side.

Divide $0$ by $- 5$ .

$b = 0$

$- 7 = - 7 + 8 b$

$8 = 8 - 7 b$

$- 2 = - 2 + 3 b$

$a = 1 - b$

$b = 0$

$- 7 = - 7 + 8 b$

$8 = 8 - 7 b$

$- 2 = - 2 + 3 b$

$a = 1 - b$

$b = 0$

$- 7 = - 7 + 8 b$

$8 = 8 - 7 b$

$- 2 = - 2 + 3 b$

$a = 1 - b$

$b = 0$

$- 7 = - 7 + 8 b$

$8 = 8 - 7 b$

$- 2 = - 2 + 3 b$

$a = 1 - b$

Replace all occurrences of $b$ with $0$ in each equation.

Replace all occurrences of $b$ in $- 7 = - 7 + 8 b$ with $0$ .

$- 7 = - 7 + 8 (0)$

$b = 0$

$8 = 8 - 7 b$

$- 2 = - 2 + 3 b$

$a = 1 - b$

Simplify the right side.

Simplify $- 7 + 8 (0)$ .

Multiply $8$ by $0$ .

$- 7 = - 7 + 0$

$b = 0$

$8 = 8 - 7 b$

$- 2 = - 2 + 3 b$

$a = 1 - b$

Add $- 7$ and $0$ .

$- 7 = - 7$

$b = 0$

$8 = 8 - 7 b$

$- 2 = - 2 + 3 b$

$a = 1 - b$

$- 7 = - 7$

$b = 0$

$8 = 8 - 7 b$

$- 2 = - 2 + 3 b$

$a = 1 - b$

$- 7 = - 7$

$b = 0$

$8 = 8 - 7 b$

$- 2 = - 2 + 3 b$

$a = 1 - b$

Replace all occurrences of $b$ in $8 = 8 - 7 b$ with $0$ .

$8 = 8 - 7 \cdot 0$

$- 7 = - 7$

$b = 0$

$- 2 = - 2 + 3 b$

$a = 1 - b$

Simplify the right side.

Simplify $8 - 7 \cdot 0$ .

Multiply $- 7$ by $0$ .

$8 = 8 + 0$

$- 7 = - 7$

$b = 0$

$- 2 = - 2 + 3 b$

$a = 1 - b$

Add $8$ and $0$ .

$8 = 8$

$- 7 = - 7$

$b = 0$

$- 2 = - 2 + 3 b$

$a = 1 - b$

$8 = 8$

$- 7 = - 7$

$b = 0$

$- 2 = - 2 + 3 b$

$a = 1 - b$

$8 = 8$

$- 7 = - 7$

$b = 0$

$- 2 = - 2 + 3 b$

$a = 1 - b$

Replace all occurrences of $b$ in $- 2 = - 2 + 3 b$ with $0$ .

$- 2 = - 2 + 3 (0)$

$8 = 8$

$- 7 = - 7$

$b = 0$

$a = 1 - b$

Simplify the right side.

Simplify $- 2 + 3 (0)$ .

Multiply $3$ by $0$ .

$- 2 = - 2 + 0$

$8 = 8$

$- 7 = - 7$

$b = 0$

$a = 1 - b$

Add $- 2$ and $0$ .

$- 2 = - 2$

$8 = 8$

$- 7 = - 7$

$b = 0$

$a = 1 - b$

$- 2 = - 2$

$8 = 8$

$- 7 = - 7$

$b = 0$

$a = 1 - b$

$- 2 = - 2$

$8 = 8$

$- 7 = - 7$

$b = 0$

$a = 1 - b$

Replace all occurrences of $b$ in $a = 1 - b$ with $0$ .

$a = 1 - (0)$

$- 2 = - 2$

$8 = 8$

$- 7 = - 7$

$b = 0$

Simplify the right side.

Subtract $0$ from $1$ .

$a = 1$

$- 2 = - 2$

$8 = 8$

$- 7 = - 7$

$b = 0$

$a = 1$

$- 2 = - 2$

$8 = 8$

$- 7 = - 7$

$b = 0$

$a = 1$

$- 2 = - 2$

$8 = 8$

$- 7 = - 7$

$b = 0$

Remove any equations from the system that are always true.

$a = 1$

$b = 0$

List all of the solutions.

$a = 1, b = 0$

Calculate the value of $y$ using each $x$ value in the relation and compare this value to the given $y$ value in the relation.

Calculate the value of $y$ when $a = 1$ , $b = 0$ , and $x = - 2$ .

Multiply $- 2$ by $1$ .

$y = - 2 + 0$

Add $- 2$ and $0$ .

$y = - 2$

If the table has a linear function rule, $y = y$ for the corresponding $x$ value, $x = - 2$ . This check passes since $y = - 2$ and $y = - 2$ .

$- 2 = - 2$

Calculate the value of $y$ when $a = 1$ , $b = 0$ , and $x = 8$ .

Multiply $8$ by $1$ .

$y = 8 + 0$

Add $8$ and $0$ .

$y = 8$

If the table has a linear function rule, $y = y$ for the corresponding $x$ value, $x = 8$ . This check passes since $y = 8$ and $y = 8$ .

$8 = 8$

Calculate the value of $y$ when $a = 1$ , $b = 0$ , and $x = - 7$ .

Multiply $- 7$ by $1$ .

$y = - 7 + 0$

Add $- 7$ and $0$ .

$y = - 7$

If the table has a linear function rule, $y = y$ for the corresponding $x$ value, $x = - 7$ . This check passes since $y = - 7$ and $y = - 7$ .

$- 7 = - 7$

Calculate the value of $y$ when $a = 1$ , $b = 0$ , and $x = 1$ .

Multiply $1$ by $1$ .

$y = 1 + 0$

Add $1$ and $0$ .

$y = 1$

If the table has a linear function rule, $y = y$ for the corresponding $x$ value, $x = 1$ . This check passes since $y = 1$ and $y = 1$ .

$1 = 1$

Calculate the value of $y$ when $a = 1$ , $b = 0$ , and $x = 6$ .

Multiply $6$ by $1$ .

$y = 6 + 0$

Add $6$ and $0$ .

$y = 6$

If the table has a linear function rule, $y = y$ for the corresponding $x$ value, $x = 6$ . This check passes since $y = 6$ and $y = 6$ .

$6 = 6$

Since $y = y$ for the corresponding $x$ values, the function is linear.

The function is linear

Since all $y = y$ , the function is linear and follows the form $y = x$ .

$y = x$

Find $x + 9$ .

Use the function rule equation to find $x + 9$ .

$10 x + 9 = x + 9$

Move all terms containing $x$ to the left side of the equation.

Subtract $x$ from both sides of the equation.

$10 x + 9 - x = 9$

Subtract $x$ from $10 x$ .

$9 x + 9 = 9$

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

Subtract $9$ from both sides of the equation.

$9 x = 9 - 9$

Subtract $9$ from $9$ .

$9 x = 0$

Divide each term in $9 x = 0$ by $9$ and simplify.

Divide each term in $9 x = 0$ by $9$ .

$\frac{9 x}{9} = \frac{0}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x}{9} = \frac{0}{9}$

Divide $x$ by $1$ .

$x = \frac{0}{9}$

Simplify the right side.

Divide $0$ by $9$ .

$x = 0$

Find $- 9 y$ .

Use the function rule equation to find $- 9 y$ .

$- 36 = - 9 y$

Rewrite the equation as $- 9 y = - 36$ .

$- 9 y = - 36$

Divide each term in $- 9 y = - 36$ by $- 9$ and simplify.

Divide each term in $- 9 y = - 36$ by $- 9$ .

$\frac{- 9 y}{- 9} = \frac{- 36}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 y}{- 9} = \frac{- 36}{- 9}$

Divide $y$ by $1$ .

$y = \frac{- 36}{- 9}$

Simplify the right side.

Divide $- 36$ by $- 9$ .

$y = 4$

Find $- 2 x$ .

Use the function rule equation to find $- 2 x$ .

$- 2 = - 2 x$

Rewrite the equation as $- 2 x = - 2$ .

$- 2 x = - 2$

Divide each term in $- 2 x = - 2$ by $- 2$ and simplify.

Divide each term in $- 2 x = - 2$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- 2}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- 2}{- 2}$

Divide $x$ by $1$ .

$x = \frac{- 2}{- 2}$

Simplify the right side.

Divide $- 2$ by $- 2$ .

$x = 1$

Find $y - 5$ .

Use the function rule equation to find $y - 5$ .

$- 1 = y - 5$

Rewrite the equation as $y - 5 = - 1$ .

$y - 5 = - 1$

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

Add $5$ to both sides of the equation.

$y = - 1 + 5$

Add $- 1$ and $5$ .

$y = 4$

List all of the solutions.

$x = 0 y = 4 x = 1 y = 4$

Solve the Matrix Equation [[x+9,-2,-9y],[8,-2x,-7],[1,y-5,6]]=[[10x+0,-2,-36],[8,-2,-7],[1,-1,6]]

Related Questions

Support LCMGCF.com by disabling your adblocker.