Algebra and Trigonometry 10th Edition

$x= -7; y=-4$
The system can be written as: $AX=B$ where, $B= \begin{bmatrix} x \\ y \end{bmatrix}$ When there is an inverse of a matrix $A A^{-1} = I$ (the Identity Matrix) Thus, $X=A^{-1} B = \begin{bmatrix} -3 &2 \\ -2 & 1 \end{bmatrix} \begin{bmatrix} 1 \\ -2 \end{bmatrix} = \begin{bmatrix} (-3) (1)+(2)(-2) \\ (-2) (1) +(1)(-2) \end{bmatrix}=\begin{bmatrix} -7 \\ -4 \end{bmatrix}$ So, $X= \begin{bmatrix} x \\ y \end{bmatrix}=\begin{bmatrix} -7 \\ -4 \end{bmatrix}$ Therefore, $x= -7; y=-4$