Answer
$(x,y)=(-1,-3)$
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,
$D=\begin{vmatrix}1&-2\\5&-1\end{vmatrix}=9$
and
$D_x=\begin{vmatrix}5&-2\\-2&-1\end{vmatrix}=-9$
Also,
$D_y=\begin{vmatrix}1&5\\5&-2\end{vmatrix}=-27$
Now, $x=\dfrac{D_x}{D}=-1$ and $y=\dfrac{D_y}{D}=-3$
Hence, $(x,y)=(-1,-3)$
