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The straight lines given by the equation 2x^2=2y^2-3xy are: 21 Mar 2019, 13:19
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49% (02:03) correct 51% (02:01) wrong based on 113 sessions

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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 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
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E
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The straight lines given by the equation 2x^2=2y^2-3xy are: 21 Mar 2019, 14:47
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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 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
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\(?\,\,:\,\,{\rm{lines}}\,\,{\rm{relative}}\,\,{\rm{position}}\)


\(2{x^2} = 2{y^2} - 3xy\,\,\,\, \Leftrightarrow \,\,\,\,2{x^2} - xy = 2{y^2} - 4xy\,\,\,\, \Leftrightarrow\)

\(\Leftrightarrow \,\,\,\,x\left( {2x - y} \right) = - 2y\left( { - y + 2x} \right)\,\,\,\, \Leftrightarrow \,\,\,\,\left( {2x - y} \right)\left( {x + 2y} \right) = 0\)

\(\left( {2x - y} \right)\left( {x + 2y} \right) = 0\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\left\{ \matrix{\\
\,2x - y = 0 \hfill \cr \\
\,\,{\rm{or}} \hfill \cr \\
\,x + 2y = 0 \hfill \cr} \right.\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\left\{ \matrix{\\
\,y = 2x\,\,\,\,\left( {{\rm{slope}} = 2} \right) \hfill \cr \\
\,\,{\rm{or}} \hfill \cr \\
\,y = - {x \over 2}\,\,\,\,\left( {{\rm{slope}} = - {1 \over 2}} \right) \hfill \cr} \right.\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( {\rm{E}} \right)\)


We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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The straight lines given by the equation 2x^2=2y^2-3xy are: 21 Mar 2019, 17:44
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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 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.
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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^2-3xy are: 21 Mar 2019, 18:03
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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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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 first-degree 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 second-degree 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 second-degree 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^2-3xy are: 24 Jan 2025, 03:59
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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 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
Show more

\(2{y^2} -3xy -2{x^2} =0 \)

\(2 {y^2} -4xy+xy- 2{x^2}=0\)

\(2y(y-2x)+x(y-2x)=0\)

\((y-2x) + (2y+x)=0\)

\(y=2x\) and \(y=-\frac{1}{2}x\), are the two lines.

Since the product of their slopes = \(-1,\) thus the two lines are perpendicular.

Ans E

Hope it helped.
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The straight lines given by the equation 2x^2=2y^2-3xy are: 21 Apr 2026, 10:57
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