Answer
See below
Work Step by Step
According to Cramer's Rule for a $2\times 2$ system $Ax=b$ where $A=\begin{bmatrix}
a_1 &b_1\\a_2&b_2
\end{bmatrix}$ and $b=\begin{bmatrix}
c_1\\c_2
\end{bmatrix}$
we have $x_1=\frac{\begin{vmatrix}
c_1 &b_1\\c_2&b_2
\end{vmatrix}}{\begin{vmatrix}
a_1 &b_1\\a_2&b_2
\end{vmatrix}}=\frac{\begin{vmatrix}
0 &8\\-3&4
\end{vmatrix}}{\begin{vmatrix}
2 &8\\ -2&4
\end{vmatrix}}=\frac{0+24}{8+16}=1$
and $x_2=\frac{\begin{vmatrix}
a_1 &c_1\\a_2&c_2
\end{vmatrix}}{\begin{vmatrix}
a_1 &b_1\\a_2&b_2
\end{vmatrix}}=\frac{\begin{vmatrix}
2 &0\\-2&3
\end{vmatrix}}{\begin{vmatrix}
2 &8\\ -2&4
\end{vmatrix}}=\frac{-6+0}{8+16}=\frac{1}{4}$
