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

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Question 126151: Solve the system by graphing.
3x – y = 1
3x – y = 2
please help
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!


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.