Question

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

Answer 1

`x + y = (1000)/(9)`

Explanation:

Step 1: Identify the approach:

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

Step 2: Analyze:

`9x + 2y^(2) - 3z^(2) = 132\\9y - 2y^(2) + 3z^(2) = 867`

Realize that in both equations, the
`2y^(2)` and
`3z^(2)` are in form of different signs. Then adding up corresponding sides of both equation can help eliminate these undesired components.

Step 3: Perform manipulation:

`9x + 2y^(2) - 3z^(2) + 9y - 2y^(2) - 3z^(2) = 132 + 867`

Rearrange:

`(9x + 9y) + (2y^(2) - 2y^(2)) +(3z^(2) - 3z^(2)) = 132 + 867`

Simplify:

`9(x + y) + 0 + 0 = 1000`

Simplify:

`x + y = (1000)/(9)`

Hope this helps!

:)