Find the Variables [[x],[y]]=[[-3,5],[-1,2]][[0],[2]]

$[\begin{array}{c} x \\ y \end{array}] = [\begin{array}{c} - 3 & 5 \\ - 1 & 2 \end{array}] [\begin{array}{c} 0 \\ 2 \end{array}]$

Step 1

Simplify the right side of the equation.

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

$[\begin{array}{c} x \\ y \end{array}] = [\begin{array}{c} - 3 \cdot 0 + 5 \cdot 2 \\ - 1 \cdot 0 + 2 \cdot 2 \end{array}]$

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

$[\begin{array}{c} x \\ y \end{array}] = [\begin{array}{c} 10 \\ 4 \end{array}]$

Step 2

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

$x = 10$

$y = 4$

Step 3

The system is already solved.

$x = 10, y = 4$