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The straight lines given by the equation 2x^2=2y^23xy are:
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21 Mar 2019, 13:19
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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 30degrees angle (C) intersecting and they form a 45degrees angle (D) intersecting and they form a 60degrees angle (E) intersecting and they form a 90degrees angle
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Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our highlevel "quant" preparation starts here: https://gmath.net



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Re: The straight lines given by the equation 2x^2=2y^23xy are:
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21 Mar 2019, 14:47
fskilnik 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 30degrees angle (C) intersecting and they form a 45degrees angle (D) intersecting and they form a 60degrees angle (E) intersecting and they form a 90degrees 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.
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Re: The straight lines given by the equation 2x^2=2y^23xy are:
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21 Mar 2019, 17:44
fskilnik wrote: fskilnik 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 30degrees angle (C) intersecting and they form a 45degrees angle (D) intersecting and they form a 60degrees angle (E) intersecting and they form a 90degrees 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. Hi, Is not it the equation above second degree that does present a line? As I know, an equation of line is first degree. Can you help please with more details?



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The straight lines given by the equation 2x^2=2y^23xy are:
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21 Mar 2019, 18:03
Mo2men wrote: Hi, Is not it the equation above second degree that does present a line? As I know, an equation of line is first degree. Can you help please with more details?
Hi Mo2men, Thank you for your interest in our problem and in my solution. I will not go into many details about the relationship between lines and firstdegree equations, because all that it is needed to know (in GMAT´s scope) is contained in our course. On the other hand, please notice that the set of points (x,y) in the rectangular coordinate system, associated with the solution set of the seconddegree equation presented in the question stem, is exactly the reunion of TWO intersecting lines, not just one line. In other words, your intuition/knowledge is not refuted: the seconddegree equation presented in the question stem is NOT related to a SINGLE straight line! Regards and success in your studies, Fabio.
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The straight lines given by the equation 2x^2=2y^23xy are:
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21 Mar 2019, 18:03






