SOLUTION: Solve the system of equations 2x+y=1 4x+2y=3 My answer is that there is no solution. Is that correct and if not what am I doing wrong?

Question 218986: Solve the system of equations
2x+y=1
4x+2y=3
My answer is that there is no solution. Is that correct and if not what am I doing wrong?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
you are correct.
There is no solution.
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Reason was that you wound upo with 0 + 0 = 1 which is not true.
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Your two equations are:
2x + y = 1
4x + 2y = 3
Multiply both sides of the first equation to get:
4x + 2y = 2
4x + 2y = 3
Subtract first equation from the second equation to get:
0 + 0 = 1
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Statement is not true, therefore no solutions.
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Your equations turn out to be parallel lines.
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Converting both of them from the standard form of ax + by = c to the slope-intercept form of y = mx + b, I get
y = -2x + 1
y = -2x + 3/2
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m is the slope.
b is the y-intercept
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Your slopes are equal which indicates that the lines are parallel.
-----
graph of both of these equations is:

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