ASAP1. 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 =
Accepted Solution
A:
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
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.