SOLUTION: show graph one soulution, no solution or many solutions x + y =-3 2x-y= -3

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Question 117422: show graph one soulution, no solution or many solutions
x + y =-3
2x-y= -3
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

2x-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=-3 Start with the given equation



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



1y=-x-3 Rearrange the equation



y=%28-x-3%29%2F%281%29 Divide both sides by 1



y=%28-1%2F1%29x%2B%28-3%29%2F%281%29 Break up the fraction



y=-x-3 Reduce



Now lets graph y=-x-3 (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-3%29+ Graph of y=-x-3




So let's solve for y on the second equation


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



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



-y=-2x-3 Rearrange the equation



y=%28-2x-3%29%2F%28-1%29 Divide both sides by -1



y=%28-2%2F-1%29x%2B%28-3%29%2F%28-1%29 Break up the fraction



y=2x%2B3 Reduce





Now lets add the graph of y=2x%2B3 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-x-3%2C2x%2B3%29+ Graph of y=-x-3(red) and y=2x%2B3(green)


From the graph, we can see that the two lines intersect at the point (-2,-1) (note: you might have to adjust the window to see the intersection)