Answer
$(x,y)=(5,2)$
Work Step by Step
General formula to calculate the determinant of matrix is:
$D=\begin{vmatrix}p&q\\r&s\end{vmatrix}=ps-qr$
From question, we have $D=\begin{vmatrix}1&1\\1&-1\end{vmatrix}=(1)(-1)-(1)(1)=-2$
Now,
$D_x=\begin{vmatrix}7&1\\3&-1\end{vmatrix}=(7)(-1)-(3)(1)=-10$
and
$D_y=\begin{vmatrix}1&7\\1&3\end{vmatrix}=(1)(3)-(7)(3)=-4$
Apply Cramer's Rule which states that
$x=\dfrac{D_x}{D}$ and $y=\dfrac{D_y}{D}$
Therefore, $x=\dfrac{D_x}{D}=\dfrac{-10}{-2}=5$ and $y=\dfrac{D_y}{D}=\dfrac{-4}{-2}=2$
Hence, our answer is: $(x,y)=(5,2)$
