SOLUTION: Solve the system by graphing. 3x – y = 1 3x – y = 2

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Question 109871: Solve the system by graphing.
3x – y = 1
3x – y = 2
Found 2 solutions by jim_thompson5910, MathLover1:
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:


3x-y=1

3x-y=2





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


3x-y=1 Start with the given equation



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



-y=-3x%2B1 Rearrange the equation



y=%28-3x%2B1%29%2F%28-1%29 Divide both sides by -1



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



y=3x-1 Reduce



Now lets graph y=3x-1 (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+3x-1%29+ Graph of y=3x-1




So let's solve for y on the second equation


3x-y=2 Start with the given equation



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



-y=-3x%2B2 Rearrange the equation



y=%28-3x%2B2%29%2F%28-1%29 Divide both sides by -1



y=%28-3%2F-1%29x%2B%282%29%2F%28-1%29 Break up the fraction



y=3x-2 Reduce





Now lets add the graph of y=3x-2 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+3x-1%2C3x-2%29+ Graph of y=3x-1(red) and y=3x-2(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.

Answer by MathLover1(20855) 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:


3x-y=1

3x-y=2





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


3x-y=1 Start with the given equation



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



-y=-3x%2B1 Rearrange the equation



y=%28-3x%2B1%29%2F%28-1%29 Divide both sides by -1



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



y=3x-1 Reduce



Now lets graph y=3x-1 (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+3x-1%29+ Graph of y=3x-1




So let's solve for y on the second equation


3x-y=2 Start with the given equation



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



-y=-3x%2B2 Rearrange the equation



y=%28-3x%2B2%29%2F%28-1%29 Divide both sides by -1



y=%28-3%2F-1%29x%2B%282%29%2F%28-1%29 Break up the fraction



y=3x-2 Reduce





Now lets add the graph of y=3x-2 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+3x-1%2C3x-2%29+ Graph of y=3x-1(red) and y=3x-2(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.