Answer
$x=3, y=1$
Work Step by Step
Rewrite our system of equations in matrix form:
$\begin{bmatrix}
3 & -4\\
2 & -3
\end{bmatrix}.\begin{bmatrix}
x\\
y
\end{bmatrix}=\begin{bmatrix}
5\\
3
\end{bmatrix}$
$\begin{bmatrix}
x\\
y
\end{bmatrix}=\frac{1}{-9+8}\begin{bmatrix}
-3&4\\
-2 & 3
\end{bmatrix}.\begin{bmatrix}
5\\
3
\end{bmatrix}$
$\begin{bmatrix}
x\\
y
\end{bmatrix}=-1\begin{bmatrix}
-3\\
-1
\end{bmatrix}$
$\begin{bmatrix}
x\\
y
\end{bmatrix}=\begin{bmatrix}
3\\
1
\end{bmatrix}$
Hence, $x=3, y=1$
