Answer
$x=2, y=-5$
Work Step by Step
Write the linear system as a matrix equation $AX = B$.
$\begin{bmatrix}
5 & 3\\
-9&-6
\end{bmatrix}\begin{bmatrix}
x\\
y
\end{bmatrix}=\begin{bmatrix}
-5\\
12
\end{bmatrix}$
Then
$\begin{bmatrix}
x\\
y
\end{bmatrix}=\frac{1}{-30+27}\begin{bmatrix}
-6 & -3\\
9&5
\end{bmatrix}\begin{bmatrix}
-5\\
12
\end{bmatrix}$
$\begin{bmatrix}
x\\
y
\end{bmatrix}=\frac{-1}{3}\begin{bmatrix}
-6\\
15
\end{bmatrix}$
$\begin{bmatrix}
x\\
y
\end{bmatrix}=\begin{bmatrix}
2\\
-5
\end{bmatrix}$
Hence, $x=2, y=-5$
