Question 895469
3x-y+2z=12,
x+2y+3z=11,
2x-2y-z=2


3,-1,2,12
1,2,3,11
2,-2,-1,2

divide row 1 by 3
1,-1/3,2/3,4
1,2,3,11
2,-2,-1,2

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

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

divide row 2 by 7/3
1,-1/3,2/3,4
0,1,1,3
0,-4/3,-7/3,-6

add  down (4/3) *row 2 to row 3
1,-1/3,2/3,4
0,1,1,3
0,0,-1,-2

divide row 3 by -1
1,-1/3,2/3,4
0,1,1,3
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  (-1) *row 3 to row 2
1,-1/3,2/3,4
0,1,0,1
0,0,1,2

add up  (-2/3) *row 3 to row 1
1,-3/9,0,8/3
0,1,0,1
0,0,1,2

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

final
1,0,0,3
0,1,0,1
0,0,1,2

1,0,0,3
0,1,0,1
0,0,1,2
"3","1","2"
(3,1,2)