Answer
$x=-6, y=10$
Work Step by Step
Rewrite our system of equations in matrix form:
$\begin{bmatrix}
2& 1\\
2& 5
\end{bmatrix}.\begin{bmatrix}
x\\
y
\end{bmatrix}=\begin{bmatrix}
-2\\
38
\end{bmatrix}$
$\begin{bmatrix}
x\\
y
\end{bmatrix}=\frac{1}{10-2}\begin{bmatrix}
5 & -1\\
-2&2
\end{bmatrix}.\begin{bmatrix}
-2\\
38
\end{bmatrix}$
$\begin{bmatrix}
x\\
y
\end{bmatrix}=\frac{1}{8}\begin{bmatrix}
-48\\
80
\end{bmatrix}$
$\begin{bmatrix}
x\\
y
\end{bmatrix}=\begin{bmatrix}
-6\\
10
\end{bmatrix}$
Hence, $x=-6, y=10$
