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# If x + y = 2, and x^2 - xy - 10 - 2y^2 = 0, what does x - 2y

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Director
Joined: 12 Jun 2006
Posts: 536
Followers: 1

Kudos [?]: 29 [0], given: 1

If x + y = 2, and x^2 - xy - 10 - 2y^2 = 0, what does x - 2y [#permalink]  27 Oct 2006, 15:15
If x + y = 2, and x^2 - xy - 10 - 2y^2 = 0, what does x - 2y equal?

A) 0
B) 1
C) 2
D) 5
E) 10

Can I substitute -y + 2 for x in the second equation? If not, why?
VP
Joined: 25 Jun 2006
Posts: 1175
Followers: 2

Kudos [?]: 72 [0], given: 0

D.

the long equation is basically (x+y)(x-2y) = 10.
then u get the answer instantly.
Senior Manager
Joined: 30 Aug 2006
Posts: 374
Followers: 3

Kudos [?]: 20 [0], given: 0

yep 5

(x + y)(x - 2y) = 10

x^2 + -2xy + xy - 2y^2 = 10

x^2 - xy - 2y^2 = 10
Director
Joined: 12 Jun 2006
Posts: 536
Followers: 1

Kudos [?]: 29 [0], given: 1

Thanks for the answers. But I wanted to know why substitution didn't seem to work here. I tried substituting -y + 2 for x in the second equation, x^2 - xy - 10 - 2y^2 = 0.

I do realize that the 2nd equation is a quadratic and we can and prob should solve this prob. using the above method. I'm just curious whether any alternate solutions would work.
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