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

With this problem, the general solution is to try manipulate given data and transform data into a new form, in which, the desired value [tex](x + y)[/tex] is on the left side and all of other components which do not contain [tex]x[/tex] or [tex]y[/tex] are on the right side.

Step 2: Analyze:

[tex]9x + 2y^{2} - 3z^{2} = 132\\9y - 2y^{2} + 3z^{2} = 867[/tex]

Realize that in both equations, the [tex]2y^{2}[/tex] and [tex]3z^{2}[/tex] are in form of different signs. Then adding up corresponding sides of both equation can help eliminate these undesired components.

Step 3: Perform manipulation:

[tex]9x + 2y^{2} - 3z^{2} + 9y - 2y^{2} - 3z^{2} = 132 + 867[/tex]

Rearrange:

[tex](9x + 9y) + (2y^{2} - 2y^{2}) +(3z^{2} - 3z^{2}) = 132 + 867[/tex]

Simplify:

[tex]9(x + y) + 0 + 0 = 1000[/tex]

Simplify:

[tex]x + y = \frac{1000}{9}[/tex]

Hope this helps!

:)