SOLUTION: solve the equation by graphing. y=2x+1 , x+2y=7 ~thank you so much

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Question 458882: solve the equation by graphing. y=2x+1 , x+2y=7
~thank you so much
Answer by richwmiller(17219) 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=7

-2x%2By=1





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=7 Start with the given equation



2y=7-x Subtract +x from both sides



2y=-x%2B7 Rearrange the equation



y=%28-x%2B7%29%2F%282%29 Divide both sides by 2



y=%28-1%2F2%29x%2B%287%29%2F%282%29 Break up the fraction



y=%28-1%2F2%29x%2B7%2F2 Reduce



Now lets graph y=%28-1%2F2%29x%2B7%2F2 (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%2B7%2F2%29+ Graph of y=%28-1%2F2%29x%2B7%2F2




So let's solve for y on the second equation


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



1y=1%2B2x Add 2+x to both sides



1y=%2B2x%2B1 Rearrange the equation



y=%28%2B2x%2B1%29%2F%281%29 Divide both sides by 1



y=%28%2B2%2F1%29x%2B%281%29%2F%281%29 Break up the fraction



y=2x%2B1 Reduce





Now lets add the graph of y=2x%2B1 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%28-1%2F2%29x%2B7%2F2%2C2x%2B1%29+ Graph of y=%28-1%2F2%29x%2B7%2F2(red) and y=2x%2B1(green)


From the graph, we can see that the two lines intersect at the point (1,3) (note: you might have to adjust the window to see the intersection)