SOLUTION: One last question for the day. How would you solve the system by graphing x+y=3 and x+y=-1

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Question 90362: One last question for the day. How would you solve the system by graphing
x+y=3 and x+y=-1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


1x%2By=3

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



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



1y=-x-1 Rearrange the equation



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



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



y=-x-1 Reduce





Now lets add the graph of y=-x-1 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-x%2B3%2C-x-1%29+ Graph of y=-x%2B3(red) and y=-x-1(green)


From the graph, we can see that the two lines are parallel and will never intersect. So there are no solutions and the system is inconsistent.