Answer
$\left( x,y \right)=\left( 1,-2 \right)$.
Work Step by Step
According to Cramer’s rule
$x=\frac{{{D}_{x}}}{D}$, $y=\frac{{{D}_{y}}}{D}$
As
$\begin{align}
& D=\left| \begin{matrix}
4 & 1 \\
2 & -3 \\
\end{matrix} \right| \\
& {{D}_{x}}=\left| \begin{matrix}
2 & 1 \\
8 & -3 \\
\end{matrix} \right| \\
& {{D}_{y}}=\left| \begin{matrix}
4 & 2 \\
2 & 8 \\
\end{matrix} \right|
\end{align}$
Calculate the given determinants.
$\begin{align}
& D=\left| \begin{matrix}
4 & 1 \\
2 & -3 \\
\end{matrix} \right| \\
& =-12-2 \\
& =-14
\end{align}$
$\begin{align}
& {{D}_{x}}=\left| \begin{matrix}
2 & 1 \\
8 & -3 \\
\end{matrix} \right| \\
& =-6-8 \\
& =-14
\end{align}$
$\begin{align}
& {{D}_{y}}=\left| \begin{matrix}
4 & 2 \\
2 & 8 \\
\end{matrix} \right| \\
& =32-4 \\
& =28
\end{align}$
Substitute the given values
$\begin{align}
& x=\frac{{{D}_{x}}}{D} \\
& =\frac{-14}{-14} \\
& =1
\end{align}$
$\begin{align}
& y=\frac{{{D}_{y}}}{D} \\
& =\frac{28}{-14} \\
& =-2
\end{align}$
Therefore, $\left( x,y \right)=\left( 1,-2 \right)$
