Solve 2x-y+3z=8

Question

x-6y-z=0
-6x+3y-9z=24

Did you notice that your third equation has the same normal as the third one?

So visually I see two parallel planes intersected by third non-parallel plane, namely the second equation.

So solve equations 1 and 2, and express them in parametric form

repeat by solving equation 2 and 3

these two lines will be parallel

hint: I got direction numbers of (19,5,-11) for the lines.