Answer
$x=7, y=1$
Work Step by Step
Write the linear system as a matrix equation $AX = B$.
$\begin{bmatrix}
1 & 4 \\
2 &-5
\end{bmatrix}\begin{bmatrix}
x\\
y
\end{bmatrix}=\begin{bmatrix}
11\\
9
\end{bmatrix}$
Then multiply the matrix of constants by $A^{-1}$ on the left
$\begin{bmatrix}
x\\
y
\end{bmatrix}=\frac{1}{-5-8}\begin{bmatrix}
-5 & -4\\
-2 &1
\end{bmatrix}\begin{bmatrix}
11\\
9
\end{bmatrix}$
$\begin{bmatrix}
x\\
y
\end{bmatrix}=\frac{-1}{13}\begin{bmatrix}
-91\\
-13
\end{bmatrix}$
$\begin{bmatrix}
x\\
y
\end{bmatrix}=\begin{bmatrix}
7\\
1
\end{bmatrix}$
Hence, $x=7, y=1$
