Answer
$x=-7,y=-5$
Work Step by Step
We know that for a matrix
\[
\left[\begin{array}{rr}
a & b \\
c &d \\
\end{array} \right]
\]
the determinant, $D=ad-bc.$
Thus the determinant of the coefficient matrix: $D=5\cdot-5-1\cdot2=-25-2-27.$
Then applying Cramer's Rule: $x=\frac{\begin{vmatrix}
-40 & 1\\
11 & -5 \\
\end{vmatrix}}{5}=\frac{-40\cdot-5-1\cdot11}{-27}=\frac{189}{-27}=-7$
$y=\frac{\begin{vmatrix}
5 & -40 \\
2 & 11 \\
\end{vmatrix}}{-27}=\frac{5\cdot11-(-40)\cdot2}{-27}=\frac{135}{-27}=-5$
Thus $x=-7,y=-5$
