Question

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

Answer 1

Answer:

$x + y = \frac{1000}{9}$

Step-by-step 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:

$x + y = \frac{1000}{9}$

Hope this helps!

:)