Answer
$x=-1, y=-4$
Work Step by Step
Write the linear system as a matrix equation $AX = B$.
$\begin{bmatrix}
3 & 2\\
4&-3
\end{bmatrix}\begin{bmatrix}
x\\
y
\end{bmatrix}=\begin{bmatrix}
-11\\
8
\end{bmatrix}$
Then
$\begin{bmatrix}
x\\
y
\end{bmatrix}=\frac{1}{-9-8}\begin{bmatrix}
-3 & -2\\
-4 &3
\end{bmatrix}\begin{bmatrix}
-11\\
8
\end{bmatrix}$
$\begin{bmatrix}
x\\
y
\end{bmatrix}=\frac{-1}{17}\begin{bmatrix}
17\\
68
\end{bmatrix}$
$\begin{bmatrix}
x\\
y
\end{bmatrix}=\begin{bmatrix}
-1\\
-4
\end{bmatrix}$
Hence, $x=-1, y=-4$
