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!
The system of equations above has how many solutions?
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Given: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
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
GMAT/MBA Expert
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Another approach is to begin solving the system (using the elimination method) and see what happens.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 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