If I remember correctly it is something like this...

1) equation 1 (8x + 2y - Z = -25 ) solve for X (you will end up with a Y and a Z in the answer))

2) substitute the answer from step 1 into equation 2 (3x - 3y + 5z = 10) and solve for Z (you will end up with a Y in the answer but no X)

3) substitute the Z answer from the previous steps into equation 3 (-5x + 6y - 2z = 17) and solve for Y ( you will end up with an X in the answer but no Z)

4) substitute the answer from step 2 and 3 in to equation 1, solving for X. This time you will get a numerical answer. Then you can solve for the remaining variables based on the answers from step 2 and 3.

Good luck!