Answer
$x= -8; y=-6$
Work Step by Step
The system can be written as: $AX=B$
where, $X= \begin{bmatrix} x \\ y \end{bmatrix}$
When there is an inverse of a matrix $A A^{-1} = I$ (the Identity Matrix)
Thus, $X=A^{-1} B = \begin{bmatrix} -3 &2 \\ -2 & 1 \end{bmatrix}
\begin{bmatrix} 4 \\ 2 \end{bmatrix} = \begin{bmatrix} (-3) (4)+(2)(2) \\ (-2) (4) +(1)(2) \end{bmatrix}=\begin{bmatrix} -8 \\ -6 \end{bmatrix}$
So, $X= \begin{bmatrix} x \\ y \end{bmatrix}=\begin{bmatrix} -8 \\ -6 \end{bmatrix}$
Therefore, $x= -8; y=-6$
