Answer
$x=-5, y=-9$
Work Step by Step
Rewrite our system of equations in matrix form:
$\begin{bmatrix}
1 & -1\\
9 & -10
\end{bmatrix}.\begin{bmatrix}
x\\
y
\end{bmatrix}=\begin{bmatrix}
4\\
45
\end{bmatrix}$
$\begin{bmatrix}
x\\
y
\end{bmatrix}=\frac{1}{-10+9}\begin{bmatrix}
-10 & 1\\
-9&1
\end{bmatrix}.\begin{bmatrix}
4\\
45
\end{bmatrix}$
$\begin{bmatrix}
x\\
y
\end{bmatrix}=-1\begin{bmatrix}
5\\
9
\end{bmatrix}$
$\begin{bmatrix}
x\\
y
\end{bmatrix}=\begin{bmatrix}
-5\\
-9
\end{bmatrix}$
Hence, $x=-5, y=-9$
