SOLUTION: f(x) = 2x – 8 g(x) = ? How else can you describe the two lines in this inconsistent system?

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Question 473823: f(x) = 2x – 8
g(x) = ?
How else can you describe the two lines in this inconsistent system?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+2x+%96+8
g%28x%29+=+2x
you can write it as a system like this:
y=+2x+%96+8
y+=+2x
in standard form:

-2x%2By=-8
2x%2By+=0

Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


-2x%2By=8

-2x%2By=0





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%2By=8 Start with the given equation



1y=8%2B2x Add 2+x to both sides



1y=%2B2x%2B8 Rearrange the equation



y=%28%2B2x%2B8%29%2F%281%29 Divide both sides by 1



y=%28%2B2%2F1%29x%2B%288%29%2F%281%29 Break up the fraction



y=2x%2B8 Reduce



Now lets graph y=2x%2B8 (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%2B8%29+ Graph of y=2x%2B8




So let's solve for y on the second equation


-2x%2By=0 Start with the given equation



1y=0%2B2x Add 2+x to both sides



1y=%2B2x%2B0 Rearrange the equation



y=%28%2B2x%2B0%29%2F%281%29 Divide both sides by 1



y=%28%2B2%2F1%29x%2B%280%29%2F%281%29 Break up the fraction



y=2x%2B0 Reduce





Now lets add the graph of y=2x%2B0 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+2x%2B8%2C2x%2B0%29+ Graph of y=2x%2B8(red) and y=2x%2B0(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.