Answer
$x=-2, y=5$
Work Step by Step
Write the linear system as a matrix equation $AX = B$.
$\begin{bmatrix}
3 & 1\\
-1 &2
\end{bmatrix}\begin{bmatrix}
x\\
y
\end{bmatrix}=\begin{bmatrix}
-1\\
12
\end{bmatrix}$
Then
$\begin{bmatrix}
x\\
y
\end{bmatrix}=\frac{1}{6+1}\begin{bmatrix}
2 & -1\\
1 &3
\end{bmatrix}\begin{bmatrix}
-1\\
12
\end{bmatrix}$
$\begin{bmatrix}
x\\
y
\end{bmatrix}=\frac{1}{7}\begin{bmatrix}
-14\\
35
\end{bmatrix}$
$\begin{bmatrix}
x\\
y
\end{bmatrix}=\begin{bmatrix}
-2\\
5
\end{bmatrix}$
Hence, $x=-2, y=5$
