Answer
$\left( 2,-1 \right)$
Work Step by Step
According to Cramer’s rule
$x=\frac{{{D}_{x}}}{D}$, $y=\frac{{{D}_{y}}}{D}$
As
$\begin{align}
& D=\left| \begin{matrix}
2 & 1 \\
1 & -1 \\
\end{matrix} \right| \\
& {{D}_{x}}=\left| \begin{matrix}
3 & 1 \\
3 & -1 \\
\end{matrix} \right| \\
& {{D}_{y}}=\left| \begin{matrix}
2 & 3 \\
1 & 3 \\
\end{matrix} \right|
\end{align}$
Calculate the determinants.
$\begin{align}
& D=\left| \begin{matrix}
2 & 1 \\
1 & -1 \\
\end{matrix} \right| \\
& =-2-1 \\
& =-3
\end{align}$
$\begin{align}
& {{D}_{x}}=\left| \begin{matrix}
3 & 1 \\
3 & -1 \\
\end{matrix} \right| \\
& =-3-3 \\
& =-6
\end{align}$
$\begin{align}
& {{D}_{y}}=\left| \begin{matrix}
2 & 3 \\
1 & 3 \\
\end{matrix} \right| \\
& =6-3 \\
& =3
\end{align}$
Substitute the given values
$\begin{align}
& x=\frac{{{D}_{x}}}{D} \\
& =\frac{-6}{-3} \\
& =2
\end{align}$
$\begin{align}
& y=\frac{{{D}_{y}}}{D} \\
& =\frac{3}{-3} \\
& =-1
\end{align}$
Hence, $\left( x,y \right)=\left( 2,-1 \right)$
