First of all, the first step is that I will eliminate X.
x+3y+2z=- 1
2x+3y+3z=-2
-2x+2y-3z=7
The first formula is multiplied by 2 2x+6y+4z=-2.
The second formula is 2x+3y+3z =-2.
Twice subtraction, left minus left minus right minus 3y+z=0.
The second formula 2x+3y+3z =-2.
The third formula -2x+2y-3z = 7.
Together, the two are the same, 5y=5, that is, y= 1.
Let y= 1 generation 3y+z=0 z=-3.
Then substitute y z into a formula and get x=2.