Answer
$x=4,y=-2$
Work Step by Step
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 $x=4,y=-2$
