Answer
$x=-1,y=3$
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: $D=3\cdot5-(-4)\cdot2=15+8=23.$
Then applying Cramer's Rule: $x=\frac{\begin{vmatrix}
-15 & -4 \\
13 & 5 \\
\end{vmatrix}}{23}=\frac{-15\cdot5-(-4)\cdot13}{23}=\frac{-23}{23}=-1$
$y=\frac{\begin{vmatrix}
3 & -15 \\
2 & 13 \\
\end{vmatrix}}{23}=\frac{3\cdot13-(-15)\cdot2}{23}=\frac{69}{23}=3$
Thus $x=-1,y=3$
