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How many solutions does the above system of equations have?

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Bunuel
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How many solutions does the above system of equations have? [#permalink] New post   Updated on: 07 Jul 2019, 01:18
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A
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E

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67% (00:38) correct 33% (00:52) wrong based on 182 sessions
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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

Source: Nova GMAT
Difficulty Level: 550
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E

Originally posted by Bunuel on 01 Jun 2017, 13:12.
Last edited by Sajjad1994 on 07 Jul 2019, 01:18, edited 1 time in total.
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BrentGMATPrepNow
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How many solutions does the above system of equations have? [#permalink] New post   Updated on: 05 Mar 2021, 10:38
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Bunuel 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


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

Originally posted by BrentGMATPrepNow on 01 Jun 2017, 13:26.
Last edited by BrentGMATPrepNow on 05 Mar 2021, 10:38, edited 1 time in total.
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Re: How many solutions does the above system of equations have? [#permalink] New post   01 Jun 2017, 13:22
A.. None
Both the equations are same.
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Re: How many solutions does the above system of equations have? [#permalink] New post   02 Jun 2017, 11:27
since both the equations are same,, there can be infinitely many solutions for one
same goes for the second,,,
hence E
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Re: How many solutions does the above system of equations have? [#permalink] New post   09 Dec 2020, 02:33
Given:
\(2x + y = 3\) : Equation 1
\(3y = 9 − 6x\) : Equation 2

Asked: How many solutions does the above system of equations have?

Let us multiple Equation 1 by 3
6x + 3y = 9
3y = 9 - 6x
Which is nothing but equation 2.

Both equations are same.
(x,y) will have infinite solutions.

IMO E
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Re: How many solutions does the above system of equations have? [#permalink] New post   21 Jan 2023, 16:27
Hello from the GMAT Club BumpBot!

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Re: How many solutions does the above system of equations have? [#permalink]
21 Jan 2023, 16:27
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