SOLUTION: Solve the system by graphing. x-y=2 x+y=10

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Question 83049: Solve the system by graphing.
x-y=2
x+y=10
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-y=2

1x%2By=10





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%2B2 Rearrange the equation



y=%28-x%2B2%29%2F%28-1%29 Divide both sides by -1



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



y=x-2 Reduce



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




So let's solve for y on the second equation


1x%2By=10 Start with the given equation



1y=10-x Subtract +x from both sides



1y=-x%2B10 Rearrange the equation



y=%28-x%2B10%29%2F%281%29 Divide both sides by 1



y=%28-1%2F1%29x%2B%2810%29%2F%281%29 Break up the fraction



y=-x%2B10 Reduce





Now lets add the graph of y=-x%2B10 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x-2%2C-x%2B10%29+ Graph of y=x-2(red) and y=-x%2B10(green)


From the graph, we can see that the two lines intersect at the point (6,4) (note: you might have to adjust the window to see the intersection)