Answer
$$x=-2,y=3,z=-1$$
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:
$$ M=\begin{pmatrix}2&2&1\\ -1&1&2\\ 1&2&4\end{pmatrix} \\ M_2 =\begin{pmatrix}1\\ 3\\ 0\end{pmatrix} $$
So:
$$M_x=\begin{pmatrix}1&2&1\\ 3&1&2\\ 0&2&4\end{pmatrix} \\ M_y=\begin{pmatrix}2&1&1\\ -1&3&2\\ 1&0&4\end{pmatrix} \\ M_z=\begin{pmatrix}2&2&1\\ -1&1&3\\ 1&2&0\end{pmatrix} $$
Thus:
$$ x=\frac{D_x}{D}=\frac{-18}{9} =-2 \\ y=\frac{D_y}{D}=\frac{27}{9}=3 \\ z=\frac{D_z}{D}=\frac{-9}{9} =-1 $$
