SOLUTION: Solve the system by graphing x + y = 3 x + y = –1

Algebra ->  Graphs -> SOLUTION: Solve the system by graphing x + y = 3 x + y = –1       Log On


   

Question 126088: Solve the system by graphing
x + y = 3
x + y = –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=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.