Gaussian Elimination to Solve a 3 by 3 System of Equations on Video

In this video, the Gaussian method of elimination is used to solve a 3 by 3 system of equations.
The system of equations solved is given by
\[
\begin{cases}
2x + y - z &=& 3 \\
3x - y + 2 z &=& - 11 \\
- x + 3y + z &=& 4
\end{cases}
\]