Lets solve this system of equations using addition.
9x+2y^2-3z^2=132
+ 9y-2y^2+3z^2=867
-------------------------------
9x+9y+0y^2+0z^2=999
9x+9y=999
x+y=111
Now lets break it down into two equations
x=111-y y=111-x <-- Answer
Now we can substitute with much simpler equations to check.
x=111-(111-x)
x=111-111+x
x=x
True
y=111-(111-y)
y=111-111+y
y=y
True
