Question 896649
2x-y+9x=-8
-x-3y+4z=-15
5x+2y-z=17 

Using Gauss Jordan 
2,-1,9,-8
-1,-3,4,-15
5,2,-1,17

divide row 1 by 2
1,-1/2,9/2,-4
-1,-3,4,-15
5,2,-1,17

add  down (1) *row 1 to row 2
1,-1/2,9/2,-4
0,-7/2,17/2,-19
5,2,-1,17

add  down (-5) *row 1 to row 3
1,-1/2,9/2,-4
0,-7/2,17/2,-19
0,9/2,-47/2,37

divide row 2 by -7/2
1,-1/2,9/2,-4
0,1,34/-14,-38/-7
0,9/2,-47/2,37

add  down (-9/2) *row 2 to row 3
1,-1/2,9/2,-4
0,1,17/-7,38/7
0,0,352/-28,176/14

divide row 3 by 88/-7
1,-1/2,9/2,-4
0,1,17/-7,38/7
0,0,1,-1

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

add up  (-17/-7) *row 3 to row 2
1,-1/2,9/2,-4
0,1,0,3
0,0,1,-1

add up  (-9/2) *row 3 to row 1
1,-2/4,0,1/2
0,1,0,3
0,0,1,-1

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

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

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