SOLUTION: x+y=8 2x-3y=1

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Question 144395: x+y=8
2x-3y=1
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=8
2x-3y=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%2By=8 Start with the given equation


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


1y=-x%2B8 Rearrange the equation


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


y=%28-1%2F1%29x%2B%288%29%2F%281%29 Break up the fraction


y=-x%2B8 Reduce


Now lets graph y=-x%2B8 (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%2B8%29+ Graph of y=-x%2B8



So let's solve for y on the second equation

2x-3y=1 Start with the given equation


-3y=1-2x Subtract 2+x from both sides


-3y=-2x%2B1 Rearrange the equation


y=%28-2x%2B1%29%2F%28-3%29 Divide both sides by -3


y=%28-2%2F-3%29x%2B%281%29%2F%28-3%29 Break up the fraction


y=%282%2F3%29x-1%2F3 Reduce



Now lets add the graph of y=%282%2F3%29x-1%2F3 to our first plot to get:

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-x%2B8%2C%282%2F3%29x-1%2F3%29+ Graph of y=-x%2B8(red) and y=%282%2F3%29x-1%2F3(green)

From the graph, we can see that the two lines intersect at the point (5,3)