# 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 $$w$$.
corresponds to $$x=6+\lambda-2\mu$$
and $$y=-2+2\lambda-3\mu$$