The system of equations above has how many solutions?

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

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