Answer
$(x,y)=(7,4)$
Work Step by Step
As per Cramer's Rule , we have
$x=\dfrac{D_x}{D}$ and $y=\dfrac{D_y}{D}$
The general formula to calculate the determinant of a $2 \times 2$ matrix which has 2 rows and 2 columns, such as:
$D=\begin{vmatrix}a&b\\c&d\end{vmatrix}=ad-bc$
Thus,
$D=\begin{vmatrix}2&-3\\5&4\end{vmatrix}=23$
and
$D_x=\begin{vmatrix}2&-3\\51&4\end{vmatrix}=161$
Also,
$D_y=\begin{vmatrix}2&2\\5&51\end{vmatrix}=92$
Now, $x=\dfrac{D_x}{D}=7$ and $y=\dfrac{D_y}{D}=4$
Hence, $(x,y)=(7,4)$
