Answer
$x=\frac{17}{3}, y=2$
Work Step by Step
Rewrite our system of equations in matrix form:
$\begin{bmatrix}
-3 & 2\\
6 & -5
\end{bmatrix}.\begin{bmatrix}
x\\
y
\end{bmatrix}=\begin{bmatrix}
-13\\
24
\end{bmatrix}$
$\begin{bmatrix}
x\\
y
\end{bmatrix}=\frac{1}{15-12}\begin{bmatrix}
-5&-2\\
-6 & -3
\end{bmatrix}.\begin{bmatrix}
-13\\
24
\end{bmatrix}$
$\begin{bmatrix}
x\\
y
\end{bmatrix}=\frac{1}{3}\begin{bmatrix}
17\\
6
\end{bmatrix}$
$\begin{bmatrix}
x\\
y
\end{bmatrix}=\begin{bmatrix}
\frac{17}{3}\\
2
\end{bmatrix}$
Hence, $x=\frac{17}{3}, y=2$
