I've been literally trying to solve this for more than 6 hours. I got the answers somehow, but couldn't replicate the procedure so any idea how to use the Gaussian elimination with this? I got the following matrix:

---------------------
1 1 1 1 5
-1 0 1 -1 0
0 -2 0 1 1
0 1 2 0 5
------------------

Those fucking zeros in the middle just fuck my shit up.