Answer
See below
Work Step by Step
Apply Cramer's Rule for a $3 \times 3$ system $Ax=b$ where $A=\begin{bmatrix}
a_1 & b_1 & c_1\\a_2 & b_2 & c_2\\a_3 & b_3 & c_3
\end{bmatrix}$ and $b=\begin{bmatrix}
d_1 \\ d_2 \\ d_3
\end{bmatrix}$
Obtain $x_1=\frac{\begin{vmatrix}
d_1 &b_1 & c_1\\d_2 &b_2 &c_2\\d_3 &b_3 & c_3
\end{vmatrix}}{\begin{vmatrix}
a_1 & b_1 & c_1\\a_2 & b_2 &c_2\\a_3 & b_3 & c_3
\end{vmatrix}}=\frac{\begin{vmatrix}
2 & -1&1\\ 0&5 & 3\\2 & -3 & 3
\end{vmatrix}}{\begin{vmatrix}
2 & -1 & 1\\ 4&5&3\\4 & -3&3
\end{vmatrix}}=\frac{160}{80}=2$
$x_2=\frac{\begin{vmatrix}
a_1 & d_1 & c_1\\a_2 & d_2 &c_2 \\a_3 &d_3 & c_3
\end{vmatrix}}{\begin{vmatrix}
a_1 & b_1 & c_1\\a_2 & b_2 &c_2\\a_3 & b_3 & c_3
\end{vmatrix}}=\frac{\begin{vmatrix}
4 & 0& 3\\ 2&2 & 1\\4 & 2 & 3
\end{vmatrix}}{\begin{vmatrix}
2 & -1 & 1\\ 4&5&3\\4 & -3&3
\end{vmatrix}}=\frac{4}{16}=\frac{1}{4}$
$x_3=\frac{\begin{vmatrix}
a_1 &b_1 & d_1\\a_2 &b_2 & d_2\\ a_3 &b_3 & d_3
\end{vmatrix}}{\begin{vmatrix}
a_1 & b_1 & c_1\\a_2 & b_2 &c_2\\a_3 & b_3 & c_3
\end{vmatrix}}=\frac{\begin{vmatrix}
2 & -1& 2\\ 4&5 & 0\\4 & -3 & 2
\end{vmatrix}}{\begin{vmatrix}
2 & -1 & 1\\ 4&5&3\\4 & -3&3
\end{vmatrix}}=-\frac{180}{80}=-\frac{9}{4}$
