Answer
$$x=-1,y=0,z=2$$
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:
$$ M=\begin{pmatrix}5&1&3\\ 1&-1&-3\\ -1&1&0\end{pmatrix} \\ M_2 =\begin{pmatrix}1\\ -7\\ 1\end{pmatrix}$$
So:
$$ M_x=\begin{pmatrix}1&1&3\\ -7&-1&-3\\ 1&1&0\end{pmatrix}\\ M_y=\begin{pmatrix}5&1&3\\ 1&-7&-3\\ -1&1&0\end{pmatrix} \\ M_z=\begin{pmatrix}5&1&1\\ 1&-1&-7\\ -1&1&1\end{pmatrix} $$
Thus:
$$ x=\frac{D_x}{D}=\frac{-18}{18}=-1 \\ y=\frac{D_y}{D}=\frac{0}{18} =0 \\ z=\frac{D_z}{D}=\frac{36}{18} =2 $$
