SOLUTION: Solve the system by graphing. x + y = 3 y = x - 5 Please help!!!!!!!!!!!!!!!!!!!!!!

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Question 136146: Solve the system by graphing.
x + y = 3
y = x - 5

Please help!!!!!!!!!!!!!!!!!!!!!!
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

x+%2B+y+=+3
y+=+x+-+5....=>...-x%2By=-5

Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


1x%2By=3

-x%2By=-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


-x%2By=-5 Start with the given equation



1y=-5%2Bx Add +x to both sides



1y=%2Bx-5 Rearrange the equation



y=%28%2Bx-5%29%2F%281%29 Divide both sides by 1



y=%28%2B1%2F1%29x%2B%28-5%29%2F%281%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) (note: you might have to adjust the window to see the intersection)