Question

ASAP

1. If 7a+3b=20 and 3a+7b=10, then what is the value of a+b?

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

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

Answer 1

Problem 1

Add the two equations

7a+3b = 20
3a+7b = 10
-----------
10a+10b = 30

Then factor out 10 from the left side
10a+10b = 30
10(a+b) = 30

Now divide both sides by 10
10(a+b) = 30
10(a+b)/10 = 30/10
a+b = 3

Final Answer: 3

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Problem 2

Add up the two equations

9x+2y^2-3z^2=132
9y-2y^2+3z^2=867
----------------
9x+9y = 999

Factor out 9 and then divide both sides by 9
9x+9y = 999
9(x+y) = 999
9(x+y)/9 = 999/9
x+y = 111

Answer: 111

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Problem 3

I'm not sure on this one. The previous tricks of adding the equations won't work because we want x-y instead of x+y. Subtracting the equations won't work because the y^2 and z^2 terms won't cancel.

I tried to use substitution but it led me in circles. There's probably some other shortcut I'm forgetting about. So I'd seek a second helper for another opinion.