Find the Variables [[-2,-5],[1,3]][[x],[y]]=[[2],[-3]]

$[\begin{array}{c} - 2 & - 5 \\ 1 & 3 \end{array}] [\begin{array}{c} x \\ y \end{array}] = [\begin{array}{c} 2 \\ - 3 \end{array}]$

Simplify the left side of the equation.

Multiply each row in the first matrix by each column in the second matrix.

$[\begin{array}{c} - 2 \cdot x - 5 \cdot y \\ 1 \cdot x + 3 \cdot y \end{array}] = [\begin{array}{c} 2 \\ - 3 \end{array}]$

Simplify each element of the matrix by multiplying out all the expressions.

$[\begin{array}{c} - 2 x - 5 y \\ x + 3 y \end{array}] = [\begin{array}{c} 2 \\ - 3 \end{array}]$

The matrix equation can be written as a set of equations.

$- 2 x - 5 y = 2$

$x + 3 y = - 3$

Subtract $3 y$ from both sides of the equation.

$x = - 3 - 3 y$

$- 2 x - 5 y = 2$

Replace all occurrences of $x$ with $- 3 - 3 y$ in each equation.

Replace all occurrences of $x$ in $- 2 x - 5 y = 2$ with $- 3 - 3 y$ .

$- 2 (- 3 - 3 y) - 5 y = 2$

$x = - 3 - 3 y$

Simplify the left side.

Simplify $- 2 (- 3 - 3 y) - 5 y$ .

Simplify each term.

Apply the distributive property.

$- 2 \cdot - 3 - 2 (- 3 y) - 5 y = 2$

$x = - 3 - 3 y$

Multiply $- 2$ by $- 3$ .

$6 - 2 (- 3 y) - 5 y = 2$

$x = - 3 - 3 y$

Multiply $- 3$ by $- 2$ .

$6 + 6 y - 5 y = 2$

$x = - 3 - 3 y$

$6 + 6 y - 5 y = 2$

$x = - 3 - 3 y$

Subtract $5 y$ from $6 y$ .

$6 + y = 2$

$x = - 3 - 3 y$

$6 + y = 2$

$x = - 3 - 3 y$

$6 + y = 2$

$x = - 3 - 3 y$

$6 + y = 2$

$x = - 3 - 3 y$

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

Subtract $6$ from both sides of the equation.

$y = 2 - 6$

$x = - 3 - 3 y$

Subtract $6$ from $2$ .

$y = - 4$

$x = - 3 - 3 y$

$y = - 4$

$x = - 3 - 3 y$

Replace all occurrences of $y$ with $- 4$ in each equation.

Replace all occurrences of $y$ in $x = - 3 - 3 y$ with $- 4$ .

$x = - 3 - 3 \cdot - 4$

$y = - 4$

Simplify the right side.

Simplify $- 3 - 3 \cdot - 4$ .

Multiply $- 3$ by $- 4$ .

$x = - 3 + 12$

$y = - 4$

Add $- 3$ and $12$ .

$x = 9$

$y = - 4$

$x = 9$

$y = - 4$

$x = 9$

$y = - 4$

$x = 9$

$y = - 4$

List all of the solutions.

$x = 9, y = - 4$

Find the Variables [[-2,-5],[1,3]][[x],[y]]=[[2],[-3]]

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