Answer
$$x=5,y=-2,z=0$$
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:
$$ M=\begin{pmatrix}4&5&0\\ 0&3&2\\ 1&1&1\end{pmatrix} \\ M_2 = \begin{pmatrix}10\\ -6\\ 3\end{pmatrix} $$
Thus:
$$ M_x=\begin{pmatrix}10&5&0\\ -6&3&2\\ 3&1&1\end{pmatrix} \\ M_y=\begin{pmatrix}4&10&0\\ 0&-6&2\\ 1&3&1\end{pmatrix} \\ M_z=\begin{pmatrix}4&5&10\\ 0&3&-6\\ 1&1&3\end{pmatrix} $$
Hence:
$$ x=\frac{D_x}{D}=\frac{70}{14} =5 \\ y=\frac{D_y}{D}=\frac{-28}{14} =-2 \\ z=\frac{D_z}{D}=\frac{0}{14} =0 $$
