Question 912871
2x+y-z=4,
3x+5y+z=16,
x-2y-5z=3 


2,1,-1,4
3,5,1,16
1,-2,-5,3

divide row 1 by 2
1,1/2,-1/2,2
3,5,1,16
1,-2,-5,3

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

add  down (-1) *row 1 to row 3
1,1/2,-1/2,2
0,7/2,5/2,10
0,-5/2,-9/2,1

divide row 2 by 7/2
1,1/2,-1/2,2
0,1,10/14,20/7
0,-5/2,-9/2,1

add  down (5/2) *row 2 to row 3
1,1/2,-1/2,2
0,1,5/7,20/7
0,0,-76/28,114/14

divide row 3 by -19/7
1,1/2,-1/2,2
0,1,5/7,20/7
0,0,1,-3

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

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

add up  (1/2) *row 3 to row 1
1,2/4,0,1/2
0,1,0,5
0,0,1,-3

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

final
1,0,0,-2
0,1,0,5
0,0,1,-3

"-2","5","-3"
(-2,5,-3)