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system of equations

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by Robinmrtha » Wed May 13, 2009 5:53 am
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

Answer:E

If i solve i get the values for x and y..
But the question is asking me something else that i dont seem to understand...
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by dmateer25 » Wed May 13, 2009 6:17 am
x-y=3
2x=2y+6


first lets get the x and y on the same side of the 2nd equation

2x-2y=6

Now lets multiply the first equation by 2 on both sides.

2(x-y) =6
2x-2y=6


Now, we can see that the 2 equations are identical and there will be infinite number of solutions.


For example:

X can be 4 and Y 1 will be

X can be 5 and Y will be 2

and the list will go on forever.
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