Answer
$$x=-2,z=5,y=0$$
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:
$$
M=\begin{pmatrix}3&1&0\\ -1&1&-3\\ 0&1&3\end{pmatrix} \\ M_2 = \begin{pmatrix}-1\\ 7\\ 5\end{pmatrix}$$
So:
$$ M_x=\begin{pmatrix}-1&1&0\\ 7&1&-3\\ 5&1&3\end{pmatrix} \\ M_y=\begin{pmatrix}3&1&-1\\ -1&1&7\\ 0&1&5\end{pmatrix} \\ M_z=\begin{pmatrix}3&-1&0\\ -1&7&-3\\ 0&5&3\end{pmatrix} $$
Hence:
$$ x=\frac{D_x}{D}=\frac{-42}{21} = -2 \\ y=\frac{D_y}{D}=\frac{0}{21} =0 \\ z=\frac{D_z}{D}=\frac{105}{21} =5 $$
