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The system of equations has how many solutions? 3x - 6y = 9 2y - x -
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05 Mar 2021, 08:56
05 Mar 2021, 08:56
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Question Stats:
58% (01:07) correct
41% (01:25) wrong based on 48 sessions
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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
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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The system of equations has how many solutions? 3x - 6y = 9 2y - x -
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05 Mar 2021, 09:35
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
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
Cheers,
Brent
General Discussion
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
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Location: India
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Re: The system of equations has how many solutions? 3x - 6y = 9 2y - x -
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06 Mar 2021, 02:17
06 Mar 2021, 02:17
1
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
3x - 6y = 9
2y - x - 3 = 0
A. None
B. Exactly 1
C. Exactly 2
D. Exactly 3
E. Infinitely many
Here,
\(\frac{a_1}{a_2} = \frac{b_1}{b_2} ≠ \frac{c_1}{c_2}\)
i.e. \(\frac{3}{-1} = \frac{-6}{2} ≠ \frac{9}{3}\)
Therefore, we have no solution (lines are parallel)
Hence, option A
