There are infinitely many solutions but your RRE should be
1 0 -1 0 | 2
0 1 2 0 | -1
0 0 0 1 | 3
I have to use Gauss-Jordan elimination, put in reduced row echelon form and find all solutions to the following system of equations
2x - 3y - 8z = 7
-2x + 2z - w = -7
x - y - 3z + w = 6
I end up in RRE form
1 0 -1 0 | 3
0 1 2 0 | -1
0 0 0 1 | 3
I think
x = 3 + z
y = -1 - 2z
z = ???
w = 3
How can I solve the system?
Yeah, to see this just set w to be any number then you can solve it as there will be 3 equations, 3 unknowns. Change w, the rest of the solutions change, change w an infinite number of times, infinite number of solutions.
Look up Diophantine equations for similar things. (not sure how they work with systems of equations though)