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The system of equations has how many solutions? 3x - 6y = 9 2y - x -

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Carcass
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The system of equations has how many solutions? 3x - 6y = 9 2y - x - [#permalink] New post   05 Mar 2021, 08:56
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The system of equations has how many solutions?

3x - 6y = 9
2y - x - 3 = 0


A. None
B. Exactly 1
C. Exactly 2
D. Exactly 3
E. Infinitely many


Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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GreenlightTestPrep
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The system of equations has how many solutions? 3x - 6y = 9 2y - x - [#permalink] New post   05 Mar 2021, 09:35
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Carcass wrote:
The system of equations has how many solutions?

3x - 6y = 9
2y - x - 3 = 0


A. None
B. Exactly 1
C. Exactly 2
D. Exactly 3
E. Infinitely many



Given:
3x - 6y = 9
2y - x - 3 = 0

Rewrite the bottom equation as follows:
3x - 6y = 9
-x + 2y = 3

Multiply both sides of the the bottom equation by 3 to get:
3x - 6y = 9
-3x + 6y = 9

Add the two equations to get: 0x + 0y = 18
NOTE: I know this is an odd way to express the left side of the equation, but it's the easiest way to see why there are zero solutions.

Answer: A

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Brent
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Re: The system of equations has how many solutions? 3x - 6y = 9 2y - x - [#permalink] New post   06 Mar 2021, 02:17
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Carcass wrote:
The system of equations has how many solutions?

3x - 6y = 9
2y - x - 3 = 0


A. None
B. Exactly 1
C. Exactly 2
D. Exactly 3
E. Infinitely many


Here,
a1a2=b1b2≠c1c2

i.e. 3−1=−62≠93

Therefore, we have no solution (lines are parallel)

Hence, option A
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Re: The system of equations has how many solutions? 3x - 6y = 9 2y - x - [#permalink] New post   16 Jul 2023, 22:55
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Re: The system of equations has how many solutions? 3x - 6y = 9 2y - x - [#permalink]
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