Answer
$x=4; y=7$
Work Step by Step
The general form of a matrix of order $ 2 \times 2$ is:
$det \ A=\begin{vmatrix} p & q \\ r & s\end{vmatrix}=ps-qr$
Now, $|A|=\begin{vmatrix} 5 & -2 \\ -11 & 3 \end{vmatrix}=-7$
Since the determinant is not zero, we will use Cramers Rule.
$x=\dfrac{\begin{vmatrix} 6 & -2 \\ -23 & 3 \end{vmatrix}}{-7}=\dfrac{-28}{-7}=4$
and $y=\dfrac{\begin{vmatrix} 5 & 6 \\ -11 & -23 \end{vmatrix}}{-7}=\dfrac{-49}{-7}=7$
So, $x=4; y=7$
