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How many solutions does the above system of equations have?
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05 Mar 2021, 08:54
05 Mar 2021, 08:54
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\(2x + y = 3\)
\(3y = 9 − 6x\)
How many solutions does the above system of equations have?
(A) None
(B) One
(C) Two
(D) Four
(E) An infinite number
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
\(3y = 9 − 6x\)
How many solutions does the above system of equations have?
(A) None
(B) One
(C) Two
(D) Four
(E) An infinite number
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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Re: How many solutions does the above system of equations have?
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05 Mar 2021, 09:36
05 Mar 2021, 09:36
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Carcass wrote:
\(2x + y = 3\)
\(3y = 9 − 6x\)
How many solutions does the above system of equations have?
(A) None
(B) One
(C) Two
(D) Four
(E) An infinite number
\(3y = 9 − 6x\)
How many solutions does the above system of equations have?
(A) None
(B) One
(C) Two
(D) Four
(E) An infinite number
A system of 2 linear equations will have 0, 1 or infinitely many solutions.
So, we can automatically eliminate answer choices C and D
Start solving the system using the elimination method.
Given:
2x + y = 3
3y = 9 − 6x
Rearrange the bottom equation to have the same format as the top equation:
2x + y = 3
6x + 3y = 9
Take the top equation and multiply both sides by 3 to get:
6x + 3y = 9
6x + 3y = 9
Since the two equations are IDENTICAL, we can conclude that there are infinitely many solutions
Answer: E
General Discussion
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Re: How many solutions does the above system of equations have?
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06 Mar 2021, 02:13
06 Mar 2021, 02:13
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Carcass wrote:
\(2x + y = 3\)
\(3y = 9 − 6x\)
How many solutions does the above system of equations have?
(A) None
(B) One
(C) Two
(D) Four
(E) An infinite number
\(3y = 9 − 6x\)
How many solutions does the above system of equations have?
(A) None
(B) One
(C) Two
(D) Four
(E) An infinite number
Here,
\(\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}\)
i.e. \(\frac{2}{6} = \frac{1}{3} = \frac{3}{9} = \frac{1}{3}\)
Therefore, the system of equations have Infinite number of solutions.
Hence, Option E
