SOLUTION: Graph 2x-y=4 2x-y=6

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Question 111976: Graph
2x-y=4
2x-y=6
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:


2x-y=4

2x-y=6





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


2x-y=4 Start with the given equation



-y=4-2x Subtract 2+x from both sides



-y=-2x%2B4 Rearrange the equation



y=%28-2x%2B4%29%2F%28-1%29 Divide both sides by -1



y=%28-2%2F-1%29x%2B%284%29%2F%28-1%29 Break up the fraction



y=2x-4 Reduce



Now lets graph y=2x-4 (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+2x-4%29+ Graph of y=2x-4




So let's solve for y on the second equation


2x-y=6 Start with the given equation



-y=6-2x Subtract 2+x from both sides



-y=-2x%2B6 Rearrange the equation



y=%28-2x%2B6%29%2F%28-1%29 Divide both sides by -1



y=%28-2%2F-1%29x%2B%286%29%2F%28-1%29 Break up the fraction



y=2x-6 Reduce





Now lets add the graph of y=2x-6 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+2x-4%2C2x-6%29+ Graph of y=2x-4(red) and y=2x-6(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.