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 $x_1=\frac{\begin{vmatrix}
d_1 &b_1 & c_1\\d_2 &b_2 &c_2\\d_3 &b_3 & c_3
\end{vmatrix}}{\begin{vmatrix}
a_1 & b_1 & c_1\\a_2 & b_2 &c_2\\a_3 & b_3 & c_3
\end{vmatrix}}=\frac{\begin{vmatrix}
-1 & 1& 2\\ -1& -1& 1\\-5 & 5 & 5
\end{vmatrix}}{\begin{vmatrix}
3& 1 & 2\\ 2&-1& 1\\ 0 & 5 & 5
\end{vmatrix}}=\frac{10}{20}=\frac{1}{2}$
$x_2=\frac{\begin{vmatrix}
a_1 & d_1 & c_1\\a_2 & d_2 &c_2 \\a_3 &d_3 & c_3
\end{vmatrix}}{\begin{vmatrix}
a_1 & b_1 & c_1\\a_2 & b_2 &c_2\\a_3 & b_3 & c_3
\end{vmatrix}}=\frac{\begin{vmatrix}
3 & -1& 2\\ 2&-1 & 1\\ 0& -5 & 2
\end{vmatrix}}{\begin{vmatrix}
3 & 1 & 2\\ 2& -1 &1\\0 & 5&5
\end{vmatrix}}=\frac{10}{20}=\frac{1}{2}$
$x_3=\frac{\begin{vmatrix}
a_1 &b_1 & d_1\\a_2 &b_2 & d_2\\ a_3 &b_3 & d_3
\end{vmatrix}}{\begin{vmatrix}
a_1 & b_1 & c_1\\a_2 & b_2 &c_2\\a_3 & b_3 & c_3
\end{vmatrix}}=\frac{\begin{vmatrix}
3 & 1& -1\\2 &-1 & -1\\0 & 5 & -5
\end{vmatrix}}{\begin{vmatrix}
3 & 1 & 2\\ 2&-1&1\\0 & 5&5
\end{vmatrix}}=-\frac{30}{20}=-\frac{3}{2}$
