# Solving Homogeneous System using Gauss–Jordan elimination

Suppose that the augmented matrix for a system of linear equations has been reduced by row operations to the given row echelon form. Solve the system.

\begin{bmatrix}1&0&6&3&-4\\0&1&3&7&2\\0&0&1&1&4\end{bmatrix}

Let variables be $a$, $b$, $c$, $d$, $e$. You have $c=-d-4e$, $b+3c=-7d-2e$, $a+6c=-3d+4e$. Substituting from the last row in your matrix, you will obtain the solution dependent on 2 parameters: $d$ and $e$.