Question 904455
I am guessing that it should be +y in the first equation
The answers come out (23/3,22/3,10/-3) with -1y
and (1,2,-2) with +1y

 x +y-2z=7,
 2x-3y-2z=0,
 x-2y-3z=3

1,1,-2,7
2,-3,-2,0
1,-2,-3,3


add  down (-2) *row 1 to row 2
1,1,-2,7
0,-5,2,-14
1,-2,-3,3

add  down (-1) *row 1 to row 3
1,1,-2,7
0,-5,2,-14
0,-3,-1,-4

divide row 2 by -5
1,1,-2,7
0,1,2/-5,-14/-5
0,-3,-1,-4

add  down (3) *row 2 to row 3
1,1,-2,7
0,1,2/-5,14/5
0,0,11/-5,22/5

divide row 3 by 11/-5
1,1,-2,7
0,1,2/-5,14/5
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/-5) *row 3 to row 2
1,1,-2,7
0,1,0,2
0,0,1,-2

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

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

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


"1","2","-2"
(1,2,-2)