Answer
x = 7
y = -3
z = 4
Work Step by Step
NOTE: Gauss-Jordan elimination will reduce until the matrix is in reduced row-echelon form.
$\begin{bmatrix}
-1 & 1 & -1 & |-14\\
2 & -1 & 1 & |21\\
3 & 2 & 1 & |19\\
\end{bmatrix}$ ~ $\begin{bmatrix}
-1 & 1 & -1 & |-14\\
0 & 1 & -1 & |-7\\
0 & 5 & -2 & |-23\\
\end{bmatrix}$ ~ $\begin{bmatrix}
-1 & 1 & -1 & |-14\\
0 & 1 & -1 & |-7\\
0 & 0 & 3 & |12\\
\end{bmatrix}$ ~ $\begin{bmatrix}
-1 & 1 & -1 & |-14\\
0 & 1 & -1 & |-7\\
0 & 0 & 1 & |4\\
\end{bmatrix}$ ~ $\begin{bmatrix}
-1 & 1 & 0 & |-10\\
0 & 1 & 0 & |-3\\
0 & 0 & 1 & |4\\
\end{bmatrix}$ ~ $\begin{bmatrix}
1 & -1 & 0 & |10\\
0 & 1 & 0 & |-3\\
0 & 0 & 1 & |4\\
\end{bmatrix}$ ~ $\begin{bmatrix}
1 & 0 & 0 & |7\\
0 & 1 & 0 & |-3\\
0 & 0 & 1 & |4\\
\end{bmatrix}$
From reduced row-echelon form the solution is simple:
x = 7
y = -3
z = 4
