Answer
$(x,y)=(5,2)$
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 is
$D=\begin{vmatrix}a&b\\c&d\end{vmatrix}=ad-bc$
Thus,
$D=\begin{vmatrix}1&1\\1&-1\end{vmatrix}=-2$
and
$D_x=\begin{vmatrix}7&1\\3&-1\end{vmatrix}=-10$
Also,
$D_y=\begin{vmatrix}1&7\\1&3\end{vmatrix}=-4$
Now, $x=\dfrac{D_x}{D}=5$ and $y=\dfrac{D_y}{D}=2$
Hence, $(x,y)=(5,2)$
