Answer
$x=9, y=-6$
Work Step by Step
Write the linear system as a matrix equation $AX = B$.
$\begin{bmatrix}
3 & 2\\
-1&4
\end{bmatrix}\begin{bmatrix}
x\\
y
\end{bmatrix}=\begin{bmatrix}
15\\
-33
\end{bmatrix}$
Then
$\begin{bmatrix}
x\\
y
\end{bmatrix}=\frac{1}{12+2}\begin{bmatrix}
4 & -2\\
1&3
\end{bmatrix}\begin{bmatrix}
15\\
-33
\end{bmatrix}$
$\begin{bmatrix}
x\\
y
\end{bmatrix}=\frac{1}{14}\begin{bmatrix}
126\\
-84
\end{bmatrix}$
$\begin{bmatrix}
x\\
y
\end{bmatrix}=\begin{bmatrix}
9\\
-6
\end{bmatrix}$
Hence, $x=9, y=-6$
