SOLUTION: solve each system by graphing. {x-y=-2 {2x+y=8

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Question 771152: solve each system by graphing.
{x-y=-2
{2x+y=8
Answer by MathLover1(20850) 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-y=-2

2x%2By=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


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



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



-y=-x-2 Rearrange the equation



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



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



y=x%2B2 Reduce



Now lets graph y=x%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+x%2B2%29+ Graph of y=x%2B2




So let's solve for y on the second equation


2x%2By=8 Start with the given equation



1y=8-2x Subtract 2+x from both sides



1y=-2x%2B8 Rearrange the equation



y=%28-2x%2B8%29%2F%281%29 Divide both sides by 1



y=%28-2%2F1%29x%2B%288%29%2F%281%29 Break up the fraction



y=-2x%2B8 Reduce





Now lets add the graph of y=-2x%2B8 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%2B2%2C-2x%2B8%29+ Graph of y=x%2B2(red) and y=-2x%2B8(green)


From the graph, we can see that the two lines intersect at the point (2,4) (note: you might have to adjust the window to see the intersection)