SOLUTION: Solve the system by graphing. x + 2y = 4 x + 2y = –2 Please help with this graphing problem.

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Question 102506: Solve the system by graphing.
x + 2y = 4
x + 2y = –2
Please help with this graphing problem.
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


1x%2B2y=4

1x%2B2y=-2





In order to graph these equations, we need to solve for y for each equation.




So let's solve for y on the first equation


1x%2B2y=4 Start with the given equation



2y=4-x Subtract +x from both sides



2y=-x%2B4 Rearrange the equation



y=%28-x%2B4%29%2F%282%29 Divide both sides by 2



y=%28-1%2F2%29x%2B%284%29%2F%282%29 Break up the fraction



y=%28-1%2F2%29x%2B2 Reduce



Now lets graph y=%28-1%2F2%29x%2B2 (note: if you need help with graphing, check out this solver)



+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%28-1%2F2%29x%2B2%29+ Graph of y=%28-1%2F2%29x%2B2




So let's solve for y on the second equation


1x%2B2y=-2 Start with the given equation



2y=-2-x Subtract +x from both sides



2y=-x-2 Rearrange the equation



y=%28-x-2%29%2F%282%29 Divide both sides by 2



y=%28-1%2F2%29x%2B%28-2%29%2F%282%29 Break up the fraction



y=%28-1%2F2%29x-1 Reduce





Now lets add the graph of y=%28-1%2F2%29x-1 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%28-1%2F2%29x%2B2%2C%28-1%2F2%29x-1%29+ Graph of y=%28-1%2F2%29x%2B2(red) and y=%28-1%2F2%29x-1(green)


From the graph, we can see that the two lines are parallel and will never intersect. So there are no solutions and the system is inconsistent.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the system by graphing.
x + 2y = 4
x + 2y = –2
--------------------------
Comment: these lines are parallel; there is no solution for the system.
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graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C%28-1%2F2%29x%2B2%2C%28-1%2F2%29x-2%29
==================
Cheers,
Stan H.