Answer
$(x,y)=(2,-1)$
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 $D=\begin{vmatrix}2&1\\1&-1\end{vmatrix}=-2-1=-3$
Now, $D_x=\begin{vmatrix}3&1\\3&-1\end{vmatrix}=-3-3=-6$
and $D_y=\begin{vmatrix}2&3\\1&3\end{vmatrix}=6-3=3$
Apply Cramer's Rule which states that
$x=\dfrac{D_x}{D}$ and $y=\dfrac{D_y}{D}$
Therefore, $x=\dfrac{D_x}{D}=\dfrac{-6}{-3}=2$ and $y=\dfrac{D_y}{D}=\dfrac{3}{-3}=-1$
Hence, our answer is: $(x,y)=(2,-1)$
