Solve the following using Gauss-Jordan elimination:

$\displaystyle 2x+2y+2z=0$

$\displaystyle -2x+5y+2z=1$

$\displaystyle 8x+y+4z=-1$

I keep setting up augmented matrices but I do not know how to get it to reduced-eschelon form at all.

Edit: I worked this out:

$\displaystyle x=-\frac{1}{7}-\frac{3}{7}r$

$\displaystyle y=-\frac{3}{7}$

$\displaystyle z=r$

Is this correct?