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The system of equations above has how many solutions?

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by AAPL » Thu May 10, 2018 7:14 am

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Answers

A

B

C

D

E

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Difficulty—

x - y = 3
2x = 2y + 6

The system of equations above has how many solutions?

A. None
B. Exactly one
C. Exactly two
D. Exactly three
E. Infinitely many

The OA is E.

To satisfy x-y=3
(1,-2)
(2,-1)
......
Infinitely

Two equations are same.

If we think these based on function, these are same linear.

Therefore the answer is E.

Has anyone another approach to solve this PS question? Regards!
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by Brent@GMATPrepNow » Thu May 10, 2018 8:06 am
AAPL wrote:x - y = 3
2x = 2y + 6

The system of equations above has how many solutions?

A. None
B. Exactly one
C. Exactly two
D. Exactly three
E. Infinitely many
Given:
x - y = 3
2x = 2y + 6

Take 2x = 2y + 6 and divide both sides by 2 to get an EQUIVALENT equation x = y + 3
Now subtract y from both sides to get: to get another EQUIVALENT equation x - y = 3
Since this equation (x - y = 3) is identical to the other equation x - y = 3, we can be certain that ANY solution to x - y = 3 will also be a solution to x - y = 3

Since there are infinitely many solutions to x - y = 3, there will be infinitely many solutions to the SYSTEM.

Answer: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Brent@GMATPrepNow » Thu May 10, 2018 8:21 am
AAPL wrote:x - y = 3
2x = 2y + 6

The system of equations above has how many solutions?

A. None
B. Exactly one
C. Exactly two
D. Exactly three
E. Infinitely many
Another approach is to begin solving the system (using the elimination method) and see what happens.

Given:
x - y = 3
2x = 2y + 6

Take bottom equation and divide both sides by 2 to get:
x - y = 3
x = y + 3

Take bottom equation and subtract y from both sides to get:
x - y = 3
x - y = 3

Now subtract the bottom equation from the top equation to get:
0x + 0y = 0
As we can see, this equation has infinitely many solutions.

Answer: E
Brent Hanneson - Creator of GMATPrepNow.com
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