Question 904088
1,1,1,1
2,4,2,-4
-1,7,-3,-35


add  down (-2) *row 1 to row 2
1,1,1,1
0,2,0,-6
-1,7,-3,-35

add  down (1) *row 1 to row 3
1,1,1,1
0,2,0,-6
0,8,-2,-34

divide row 2 by 2
1,1,1,1
0,1,0,-3
0,8,-2,-34

add  down (-8) *row 2 to row 3
1,1,1,1
0,1,0,-3
0,0,-2,-10

divide row 3 by -2
1,1,1,1
0,1,0,-3
0,0,1,5

We now have the value for the last variable.
We will work our way up and get the other solutions.

add up  (0) *row 3 to row 2
1,1,1,1
0,1,0,-3
0,0,1,5

add up  (-1) *row 3 to row 1
1,1,0,-4
0,1,0,-3
0,0,1,5

add up  (-1) *row 2 to row 1
1,0,0,-1
0,1,0,-3
0,0,1,5

final

1,0,0,-1
0,1,0,-3
0,0,1,5
"-1","-3","5"
(-1,-3,5)