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

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

28 Feb 2012, 21:12

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

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

Hi,
Can you please help me solve the equation above

Thanks much.

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Re: If x+y=2 and x^2 - xy - 10 - 2y^2 = 0, what does x-2y =? [#permalink]

28 Feb 2012, 23:12

vintage83 wrote:

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

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

Hi,
Can you please help me solve the equation above

Thanks much.

Welcome to GMAT Club. Below is a solution to your question.

x^2-xy-10-2y^2=0 --> rearrange x^2-y^2-y^2-xy-10=0 --> apply a^6-b^2=(a-b)(a+b): (x-y)(x+y)-y^2-xy-10=0 --> (x-y)(x+y)-y(y+x)-10=0 --> factor out x+y: (x+y)(x-y-y)-10=0 --> 2(x-2y)-10=0 --> x-2y=5.

Answer: D.
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Re: If x+y=2 and x^2 - xy - 10 - 2y^2 = 0, what does x-2y =? [#permalink]

28 Feb 2012, 23:46

Very tricky....I confess...I knew there was a simpler route.....but I just did not see it.

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Re: If x+y=2 and x^2 - xy - 10 - 2y^2 = 0, what does x-2y =? [#permalink]

29 Feb 2012, 03:22

Square the first equation and subtract from the second and there you are.

You would be able to factor out and find the values of x and y. x = 3 and y = -1

x - 2y => 3 - 2(-1) = 5

BR
Mandeep

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Re: If x+y=2 and x^2 - xy - 10 - 2y^2 = 0, what does x-2y =? [#permalink]

29 Feb 2012, 07:33

Thank you very much. I get it now! I think I got confused at the last step and was stuck for a while.

Re: If x+y=2 and x^2 - xy - 10 - 2y^2 = 0, what does x-2y =? [#permalink] 29 Feb 2012, 07:33

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

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

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

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