Answer
$x=36; y=11$
Work Step by Step
The system can be written as: $AX=B$
where, $B= \begin{bmatrix} x \\ y \end{bmatrix}$
Thus, $X=A^{-1} B = \begin{bmatrix} -1 & 4 \\ 2 & -7 \end{bmatrix}
\begin{bmatrix} 8 \\ -5 \end{bmatrix} = \begin{bmatrix} (-1) (8)+(4)(-5) \\ (2) (8) +(-7)(-5) \end{bmatrix}=\begin{bmatrix} 36 \\ 11 \end{bmatrix}$
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, $X= \begin{bmatrix} x \\ y \end{bmatrix}=\begin{bmatrix} 36 \\ 11 \end{bmatrix}$
Therefore, $x=36; y=11$
