SOLUTION: Which of the following describes the graph of the solutions to the system { 2x-4y=-1 x-2y=2 I dont know if its two parallel lines, no solutions OR one line, infinately many

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Question 27856: Which of the following describes the graph of the solutions to the system
{ 2x-4y=-1
x-2y=2
I dont know if its two parallel lines, no solutions OR one line, infinately many solutions?
Thanks a bunch!
Answer by bmauger(101) About Me  (Show Source):
You can put this solution on YOUR website!
2x-4y=-1
x-2y=2
Solve the second equation for x to get:
x=2%2B2y
Substitute it into the first equation:
2x-4y=-1
2%282%2B2y%29-4y=-1
4%2B4y-4y=-1
4%3C%3E-1
Since 4 does not equal -1 there are no solutions. Meaning when you graph the equations you'll get two parallel lines.
If we put them in slope-intercept form...
2x-4y=-1Rearrange to get:
-4y=-2x-1
y=x%2F2-1%2F4
And...
x-2y=2
-2y=-x%2B2
y=x%2F2-1
So you have two lines with slope 1/2 one with an intercept -1/4 the other with an intercept of -1. Graphically:
graph%28200%2C+300%2C+-4%2C+4%2C+-4%2C+4%2C%0D%0A-x%2F2-1%2C%0D%0A-x%2F2-1%2F4%29