If 9x+2y^2−3z^2=132 and 9y−2y^2+3z^2=867, then x-y =

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

There should only be 1 solution