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