Answer
x = 8
y = 10
z = 6
Work Step by Step
NOTE: Gauss-Jordan elimination will reduce until the matrix is in reduced row-echelon form.
$\begin{bmatrix}
2 & -1 & 3 & |24\\
0 & 2 & -1 & |14\\
7 & -5 & 0 & |6\\
\end{bmatrix}$ ~ $\begin{bmatrix}
2 & -1 & 3 & |24\\
0 & 2 & -1 & |14\\
0 & -3 & -21 & |-156\\
\end{bmatrix}$ ~ $\begin{bmatrix}
2 & -1 & 3 & |24\\
0 & 2 & -1 & |14\\
0 & 1 & 7 & |52\\
\end{bmatrix}$ ~ $\begin{bmatrix}
2 & -1 & 3 & |24\\
0 & 2 & -1 & |14\\
0 & 0 & -15 & |-90\\
\end{bmatrix}$ ~ $\begin{bmatrix}
2 & -1 & 3 & |24\\
0 & 2 & -1 & |14\\
0 & 0 & 1 & |6\\
\end{bmatrix}$ ~ $\begin{bmatrix}
2 & -1 & 0 & |6\\
0 & 2 & 0 & |20\\
0 & 0 & 1 & |6\\
\end{bmatrix}$ ~ $\begin{bmatrix}
2 & -1 & 0 & |6\\
0 & 1 & 0 & |10\\
0 & 0 & 1 & |6\\
\end{bmatrix}$ ~ $\begin{bmatrix}
2 & 0 & 0 & |16\\
0 & 1 & 0 & |10\\
0 & 0 & 1 & |6\\
\end{bmatrix}$ ~ $\begin{bmatrix}
1 & 0 & 0 & |8\\
0 & 1 & 0 & |10\\
0 & 0 & 1 & |6\\
\end{bmatrix}$
From reduced row-echelon form the solution is simple:
x = 8
y = 10
z = 6
