SOLUTION: Solve the system of equations by graphing. 1=2x+y x-2y=8

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Question 82433: Solve the system of equations by graphing.
1=2x+y
x-2y=8
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:


2x%2By=1

1x-2y=8





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


2x%2By=1 Start with the given equation



1y=1-2x Subtract 2+x from both sides



1y=-2x%2B1 Rearrange the equation



y=%28-2x%2B1%29%2F%281%29 Divide both sides by 1



y=%28-2%2F1%29x%2B%281%29%2F%281%29 Break up the fraction



y=-2x%2B1 Reduce



Now lets graph y=-2x%2B1 (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+-2x%2B1%29+ Graph of y=-2x%2B1




So let's solve for y on the second equation


1x-2y=8 Start with the given equation



-2y=8-x Subtract +x from both sides



-2y=-x%2B8 Rearrange the equation



y=%28-x%2B8%29%2F%28-2%29 Divide both sides by -2



y=%28-1%2F-2%29x%2B%288%29%2F%28-2%29 Break up the fraction



y=%281%2F2%29x-4 Reduce





Now lets add the graph of y=%281%2F2%29x-4 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-2x%2B1%2C%281%2F2%29x-4%29+ Graph of y=-2x%2B1(red) and y=%281%2F2%29x-4(green)


From the graph, we can see that the two lines intersect at the point (2,-3) (note: you might have to adjust the window to see the intersection)