SOLUTION: Hi, Im a little confused with this problem. I tried to figure it out, but do not know what would be the right answer. Solve by the elimination method. 5x+6y=5 10x+12y=10 wha

Question 206622: Hi, Im a little confused with this problem. I tried to figure it out, but do not know what would be the right answer.
Solve by the elimination method.
5x+6y=5
10x+12y=10
what is the solution of the system?
( I came up with - The solution is (10,10).
but could the answer be that there are infinetely many solutions, or that there is no solution. can you please help. thanks
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
5x+6y=5
10x+12y=10
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multiply first equation by 2 to get:
10x + 12y = 10
10x + 12y = 10
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subtract second equation from first to get:
0 + 0 = 0
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I believe the answer is that this is an identity and that any value of x and y that satisfied one equation would also satisfy the other.
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if you graph both these equations, you would probably see that they are the same line.
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first equation:
5x + 6y = 5
solving for y we get:
6y -5x + 5
y = -(5/6)x + (5/6)
-----
second equation:
10x + 12y = 10
solving for y we get:
12y = -10x + 10
y = (-10/12)x + (10/12)
which can be reduced to:
y = (-5/6)x + (5/6)
-----
the equations are identical after simplification.

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