Answer
$$x=0,y=2,z=-1$$
Work Step by Step
We solve the given system of equations using Cramer's Rule. To do this, we turn the system into two matrices. We then create x, y, and z matrices by replacing the values in the original matrix with corresponding columns in the answer matrix. We then find determinants to solve. Doing this, we find:
$$ M=\begin{pmatrix}1&-2&1\\ 0&3&2\\ 3&-1&0\end{pmatrix} \\ M_2 =\begin{pmatrix}-5\\ 4\\ -2\end{pmatrix} $$
Thus:
$$ M_x=\begin{pmatrix}-5&-2&1\\ 4&3&2\\ -2&-1&0\end{pmatrix} \\M_y=\begin{pmatrix}1&-5&1\\ 0&4&2\\ 3&-2&0\end{pmatrix} \\ M_z=\begin{pmatrix}1&-2&-5\\ 0&3&4\\ 3&-1&-2\end{pmatrix}$$
So:
$$ x=\frac{D_x}{D}=\frac{0}{-19} =0 \\ y=\frac{D_y}{D}=\frac{-38}{-19}=2 \\ z=\frac{D_z}{D}=\frac{19}{-19}=-1$$
