SOLUTION: x+y=3 x-y=5

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Question 144394: x+y=3
x-y=5
Found 2 solutions by jim_thompson5910, stanbon:
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%2By=3
1x-y=5




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%2By=3 Start with the given equation


1y=3-x Subtract +x from both sides


1y=-x%2B3 Rearrange the equation


y=%28-x%2B3%29%2F%281%29 Divide both sides by 1


y=%28-1%2F1%29x%2B%283%29%2F%281%29 Break up the fraction


y=-x%2B3 Reduce


Now lets graph y=-x%2B3 (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%2B3%29+ Graph of y=-x%2B3



So let's solve for y on the second equation

1x-y=5 Start with the given equation


-y=5-x Subtract +x from both sides


-y=-x%2B5 Rearrange the equation


y=%28-x%2B5%29%2F%28-1%29 Divide both sides by -1


y=%28-1%2F-1%29x%2B%285%29%2F%28-1%29 Break up the fraction


y=x-5 Reduce



Now lets add the graph of y=x-5 to our first plot to get:

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-x%2B3%2Cx-5%29+ Graph of y=-x%2B3(red) and y=x-5(green)

From the graph, we can see that the two lines intersect at the point (4,-1)

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
x+y=3
x-y=5
----------
Add to get:
2x = 8
x = 4
------------------
Substitute to solve for y:
4+y = 3
y = -1
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Cheers,
Stan H.