How do I solve the following system of equations by using the Gauss-Jordan method? $$
\left\{\begin{array}{rcrcrcrcr}
x & - & 2y & + & 3z & - & 4w & = & 10
\\
2x & - & 3y & + & 4z & - & 5w & = & 18
\\
3x & - & 4y & + & 5z & - & 6w & = & 26 
\\
4x & - & 5y & + & 6z & - & 7w & = & 9
\end{array}\right.
$$
Tried to solve the problem and matrix came up with RREF
\begin{array}{cccc|c}1 & 0 & -1 & 2 & 6 \\0 & 1 & -2 & 3 & -2 \\0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0\end{array}

A whole line filled with 0s can be eliminated (it corresponds to equation 0=0).
The remaining system can be transformed into a square matrix if you pass to the other side the columns corresponding to $z$ and $w$.
1 0 -1 2|6
0 1 -2 3|-2
corresponds to
$x=6+\lambda-2\mu$
and $y=-2+2\lambda-3\mu$
