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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote The straight lines given by the equation 2x^2=2y^2-3xy are: tagged by: fskilnik@GMATH This topic has 1 expert reply and 0 member replies GMAT/MBA Expert The straight lines given by the equation 2x^2=2y^2-3xy are: Timer 00:00 Your Answer A B C D E Global Stats Difficult GMATH practice exercise (Quant Class 20) The straight lines given by the equation 2(x^2)=2(y^2)-3xy are: (A) parallel (B) intersecting and they form a 30-degrees angle (C) intersecting and they form a 45-degrees angle (D) intersecting and they form a 60-degrees angle (E) intersecting and they form a 90-degrees angle Answer: ______(E)__ _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 fskilnik@GMATH wrote: GMATH practice exercise (Quant Class 20) The straight lines given by the equation 2(x^2)=2(y^2)-3xy are: (A) parallel (B) intersecting and they form a 30-degrees angle (C) intersecting and they form a 45-degrees angle (D) intersecting and they form a 60-degrees angle (E) intersecting and they form a 90-degrees angle $$?\,\,:\,\,{\rm{lines}}\,\,{\rm{relative}}\,\,{\rm{position}}$$ $$2{x^2} = 2{y^2} - 3xy\,\,\,\, \Leftrightarrow \,\,\,\,2{x^2} - xy = 2{y^2} - 4xy\,\,\,\, \Leftrightarrow$$ $$\Leftrightarrow \,\,\,\,x\left( {2x - y} \right) = - 2y\left( { - y + 2x} \right)\,\,\,\, \Leftrightarrow \,\,\,\,\left( {2x - y} \right)\left( {x + 2y} \right) = 0$$ $$\left( {2x - y} \right)\left( {x + 2y} \right) = 0\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\left\{ \matrix{ \,2x - y = 0 \hfill \cr \,\,{\rm{or}} \hfill \cr \,x + 2y = 0 \hfill \cr} \right.\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\left\{ \matrix{ \,y = 2x\,\,\,\,\left( {{\rm{slope}} = 2} \right) \hfill \cr \,\,{\rm{or}} \hfill \cr \,y = - {x \over 2}\,\,\,\,\left( {{\rm{slope}} = - {1 \over 2}} \right) \hfill \cr} \right.\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( {\rm{E}} \right)$$ We follow the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br • Award-winning private GMAT tutoring Register now and save up to$200

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