SOLUTION: Solve each of the following systems by graphing. 1. 2x – y = 4 2x – y = 6

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Solve each of the following systems by graphing. 1. 2x – y = 4 2x – y = 6       Log On


   

Question 123343: Solve each of the following systems by graphing.
1. 2x – y = 4
2x – y = 6

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!


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.