Answer
x = -6
y = 8
z = 2
Work Step by Step
NOTE: Gauss-Jordan elimination will reduce until the matrix is in reduced row-echelon form.
$\begin{bmatrix}
2 & 2 & -1 & |2\\
1 & -3 & 1 & |-28\\
-1 & 1 & 0 & |14\\
\end{bmatrix}$ ~ $\begin{bmatrix}
2 & 2 & -1 & |2\\
0 & 8 & -3 & |58\\
0 & 4 & -1 & |30\\
\end{bmatrix}$ ~ $\begin{bmatrix}
2 & 2 & -1 & |2\\
0 & 8 & -3 & |58\\
0 & 0 & -1 & |-2\\
\end{bmatrix}$ ~ $\begin{bmatrix}
2 & 2 & -1 & |2\\
0 & 8 & -3 & |58\\
0 & 0 & 1 & |2\\
\end{bmatrix}$ ~ $\begin{bmatrix}
2 & 2 & 0 & |4\\
0 & 8 & 0 & |64\\
0 & 0 & 1 & |2\\
\end{bmatrix}$ ~ $\begin{bmatrix}
1 & 1 & 0 & |2\\
0 & 1 & 0 & |8\\
0 & 0 & 1 & |2\\
\end{bmatrix}$ ~ $\begin{bmatrix}
1 & 0 & 0 & |-6\\
0 & 1 & 0 & |8\\
0 & 0 & 1 & |2\\
\end{bmatrix}$
From reduced row-echelon form the solution is simple:
x = -6
y = 8
z = 2
