Answer :

1) 3x+y+z=4
2) 2x+2y+3z=3
3) x+3y+2z = 5

1)*2 6x + 2y + 2z = 8
2)    2x + 2y +3z  = 3
-   __________________
       4x - z            = 5

2)*3  6x + 6y + 9z = 9
3)*2  2x + 6y + 4z = 10
-      __________________
       4x+5z             =-1

4x+5z = -1
4x - z =5
- ________
6z = -6
z = -1

If z=-1,

4x -(-1) =5
4x = 5-1
x = 4/4
x=1

3x+y+z=4
3(1)+y+(-1)=4
3+y-1=4
y=2

So z=-1, x=1, y=2