pick 1 value to eliminate in 2 equations
let's eliminate z
add last equation to first one
2x+3y-z=2
x-3y+z=10 +
3x+0y+0z=12
3x=12
x=4
that's nice
sub that in last 2 equations and minus 4 from both sides
y-z=-2
-3y+z=6
add them
y-z=-2
-3y+z=6 +
-2y+0z=4
-2y=4
divide -2
y=-2
y=-2