SOLUTION: Please help me pick the correct answer. If x-y=6 and 3x^2+3xy-6y^2=60, then 9x+18y= Answers: a) 12 b) 15 c) 20 d) 24 e) 30

Question 121467: Please help me pick the correct answer.
If x-y=6 and 3x^2+3xy-6y^2=60, then 9x+18y=
Answers:
a) 12
b) 15
c) 20
d) 24
e) 30
Answer by algebrapro18(249) (Show Source): You can put this solution on YOUR website!
If x-y=6 and 3x^2+3xy-6y^2=60, then 9x+18y=
Answers:
a) 12
b) 15
c) 20
d) 24
e) 30

I am sure there is an easier way to do this but I can't think of one so I did it the long way. First we need to set up a system of two equations and then solve it. The system is:

x-y = 6
3x^2+3xy-6y^2 = 60

so now to solve that mess. I would start by solving the first equation for x.

x = 6+y

Now plug that into the second equation and solve for your y value.

3(6+y)^2+ 3(6+y)y-6y^2 = 60
3(6+y)(6+y) + 3y(6+y)-6y^2 = 60 <---- just rearranging some stuff here
3(36+12y+y^2) + 18y + 3y^2 - 6y^2 = 60 <--- F.O.I.L. and distribute
108 + 36y + 3y^2 + 18y + 3y^2 - 6y^2 = 60 <--- Multiplying
3y^2 + 3y^2 - 6y^2 + 36y + 18y + 108 =60 <--- rearranging
54y + 108 = 60 <--- combining like terms
54y = -48 <--- starting to solve for y, subtracting 108 from both sides
y = -48/54 <--- solving for y, dividing both sides by 54
y = -8/9 <--- simplifying the fraction

now that we have y = -8/9 we can solve for x.

x = 6 + y
x = 6 - 8/9
x = 46/9

now we can just plug in those values into 9x+18y and see what it equals.

9x+18y
= 9(46/9) + 18(-8/9)
= 46 - 16
= 30 or answer e
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