Answer
$x=-2, y=3$
Work Step by Step
Write the linear system as a matrix equation $AX = B$.
$\begin{bmatrix}
3 & 4\\
4&5
\end{bmatrix}\begin{bmatrix}
x\\
y
\end{bmatrix}=\begin{bmatrix}
6\\
7
\end{bmatrix}$
Then
$\begin{bmatrix}
x\\
y
\end{bmatrix}=\frac{1}{15-16}\begin{bmatrix}
5 & -4\\
-4 &3
\end{bmatrix}\begin{bmatrix}
6\\
7
\end{bmatrix}$
$\begin{bmatrix}
x\\
y
\end{bmatrix}=-1\begin{bmatrix}
2\\
-3
\end{bmatrix}$
$\begin{bmatrix}
x\\
y
\end{bmatrix}=\begin{bmatrix}
-2\\
3
\end{bmatrix}$
Hence, $x=-2, y=3$
