SOLUTION: Hello, can anyone help me with this? Solve the following system by graphing. x + y = 6 x - y = 3

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Question 143376: Hello, can anyone help me with this?
Solve the following system by graphing.
x + y = 6
x - y = 3
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=6
1x-y=3




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=6 Start with the given equation


1y=6-x Subtract +x from both sides


1y=-x%2B6 Rearrange the equation


y=%28-x%2B6%29%2F%281%29 Divide both sides by 1


y=%28-1%2F1%29x%2B%286%29%2F%281%29 Break up the fraction


y=-x%2B6 Reduce


Now lets graph y=-x%2B6 (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%2B6%29+ Graph of y=-x%2B6



So let's solve for y on the second equation

1x-y=3 Start with the given equation


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


-y=-x%2B3 Rearrange the equation


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


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


y=x-3 Reduce



Now lets add the graph of y=x-3 to our first plot to get:

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-x%2B6%2Cx-3%29+ Graph of y=-x%2B6(red) and y=x-3(green)

From the graph, we can see that the two lines intersect at the point (9%2F2,3%2F2) (note: using a graphing calculator will help you find the point of intersection)