Solving elementary row operations So I am faced with the following:
$$
\begin{align}
x_1 + 4x_2 - 2x_3 +8x_4 &=12\\
x_2 - 7x_3 +2x_4 &=-4\\
5x_3 -x_4 &=7\\
x_3 +3x_4 &=-5
\end{align}$$
How should I approach this problem? In other words, what is the next elementary row operation that I should attempt in order to solve it? I know how to do with 3 equations by using the augmented method but this got me a little confused. 

By the Gauss-Jordan algorithm, your next step would be to make the $4x_{2}$ into a $0$, by the Type 3 elementary row operation: multiply row 2 by -4 and add that to row 1.
