Answer
$x=-4,y=3$
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: $D=3\cdot2-5\cdot(-1)=6+5=11.$
Then applying Cramer's Rule: $x=\frac{\begin{vmatrix}
3 & 5\\
10 & 2 \\
\end{vmatrix}}{1}=\frac{3\cdot2-5\cdot10}{11}=\frac{-44}{11}=-4$
$y=\frac{\begin{vmatrix}
3 & 3 \\
-1 & 10 \\
\end{vmatrix}}{1}=\frac{3\cdot10-3\cdot-1}{11}=\frac{33}{1}=3$
Thus $x=-4,y=3$
