SOLUTION: Solve each of the following systems by graphing. 5. x – y = 8 x + y = 2

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Question 124407: Solve each of the following systems by graphing.
5.
x – y = 8
x + y = 2




Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!


Start with the given system of equations:

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


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


-y=-x%2B8 Rearrange the equation


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


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


y=x-8 Reduce


Now lets graph y=x-8 (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-8%29+ Graph of y=x-8



So let's solve for y on the second equation

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


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


1y=-x%2B2 Rearrange the equation


y=%28-x%2B2%29%2F%281%29 Divide both sides by 1


y=%28-1%2F1%29x%2B%282%29%2F%281%29 Break up the fraction


y=-x%2B2 Reduce



Now lets add the graph of y=-x%2B2 to our first plot to get:

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x-8%2C-x%2B2%29+ Graph of y=x-8(red) and y=-x%2B2(green)

From the graph, we can see that the two lines intersect at the point (5,-3) (note: you might have to adjust the window to see the intersection)