Originally Posted by
HallsofIvy Actually, it is the other way around- row reduce in order to get the echelon form.
The "augmented matrix" for this system is $\displaystyle \begin{bmatrix} 1 & 2 & 1 & 20 \\ 3 & -1 & 2 & 22 \\ 2 & 1 & -4 & 7\end{bmatrix}$.
Now use row operations to put this into echelon form. For example, a first step would be to subtract three times the first row from the second row and subtract two times the first row from the third row:
$\displaystyle \begin{matrix}1 & 2 & 1 & 20 \\ 0 & -7 & -1 & -38 \\ 0 & -3 & -6 & -33\end{bmatrix}$
That take care of the first row. Now subtract 3/7 times the second row from the third row.