Answer
$$y=1,z=2,x=1 $$
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:
$$ M=\begin{pmatrix}4&-3&0\\ -4&0&8\\ 4&1&-8\end{pmatrix} \\ M_2 = \begin{pmatrix}-2\\ 4\\ -2\end{pmatrix}$$
Thus:
$$M_x=\begin{pmatrix}4&-3&-2\\ -4&0&4\\ 4&1&-2\end{pmatrix} \\ M_y=\begin{pmatrix}-2&-3&0\\ 4&0&8\\ -2&1&-8\end{pmatrix} \\ M_z=\begin{pmatrix}4&-2&0\\ -4&4&8\\ 4&-2&-8\end{pmatrix} $$
So:
$$ x=\frac{D_x}{D}=\frac{-32}{-32}=1 \\y=\frac{D_y}{D}=\frac{-32}{-32}=1 \\ z=\frac{D_z}{D}=\frac{-64}{-32} =2 $$
