Question 918064
3,-1,-1,-15
1,2,-1,1
2,3,-2,0

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

add  down (-1) *row 1 to row 2
1,-1/3,-1/3,-5
0,7/3,-2/3,6
2,3,-2,0

add  down (-2) *row 1 to row 3
1,-1/3,-1/3,-5
0,7/3,-2/3,6
0,11/3,-4/3,10

divide row 2 by 7/3
1,-1/3,-1/3,-5
0,1,-6/21,18/7
0,11/3,-4/3,10

add  down (-11/3) *row 2 to row 3
1,-1/3,-1/3,-5
0,1,-2/7,18/7
0,0,-18/63,12/21

divide row 3 by -2/7
1,-1/3,-1/3,-5
0,1,-2/7,18/7
0,0,1,-2

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

add up  (2/7) *row 3 to row 2
1,-1/3,-1/3,-5
0,1,0,2
0,0,1,-2

add up  (1/3) *row 3 to row 1
1,-3/9,0,-17/3
0,1,0,2
0,0,1,-2

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

final
1,0,0,-5
0,1,0,2
0,0,1,-2

1,0,0,-5
0,1,0,2
0,0,1,-2
"-5","2","-2"
(-5,2,-2)