## Algebra 2 (1st Edition)

$x=4,y=-2$
We know that for a matrix $\left[\begin{array}{rr} a & b \\ c &d \\ \end{array} \right]$ the determinant is $D=ad-bc.$ Thus the determinant of the coefficient matrix is: $D=4\cdot(-2)-7\cdot(-3)=8+21=13.$ Then applying Cramer's Rule: $x=\frac{\begin{vmatrix} 2 & 7 \\ -8 & -2 \\ \end{vmatrix}}{13}=\frac{2\cdot(-2)-8\cdot(-8)}{13}=\frac{52}{13}=4$ $y=\frac{\begin{vmatrix} 4 & 2 \\ -3 & -8 \\ \end{vmatrix}}{13}=\frac{4\cdot(-8)-2\cdot(-3)}{13}=\frac{-26}{13}=-2$ Thus $x=4,y=-2$