SOLUTION: I need some help solving this system of equations by graphing.What is the solution of the system of equations, and are they consistent/independent? {{{5x-8y=40}}} {{{8y-5x=40}}

Algebra ->  Graphs -> SOLUTION: I need some help solving this system of equations by graphing.What is the solution of the system of equations, and are they consistent/independent? {{{5x-8y=40}}} {{{8y-5x=40}}      Log On


   

Question 133040: I need some help solving this system of equations by graphing.What is the solution of the system of equations, and are they consistent/independent?
5x-8y=40
8y-5x=40
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
8y-5x=40 Start with the second equation


-5x%2B8y=40 Rearrange the terms





Start with the given system of equations:

5x-8y=40
-5x%2B8y=40




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

5x-8y=40 Start with the given equation


-8y=40-5x Subtract 5+x from both sides


-8y=-5x%2B40 Rearrange the equation


y=%28-5x%2B40%29%2F%28-8%29 Divide both sides by -8


y=%28-5%2F-8%29x%2B%2840%29%2F%28-8%29 Break up the fraction


y=%285%2F8%29x-5 Reduce


Now lets graph y=%285%2F8%29x-5 (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+%285%2F8%29x-5%29+ Graph of y=%285%2F8%29x-5



So let's solve for y on the second equation

-5x%2B8y=40 Start with the given equation


8y=40%2B5x Add 5+x to both sides


8y=%2B5x%2B40 Rearrange the equation


y=%28%2B5x%2B40%29%2F%288%29 Divide both sides by 8


y=%28%2B5%2F8%29x%2B%2840%29%2F%288%29 Break up the fraction


y=%285%2F8%29x%2B5 Reduce



Now lets add the graph of y=%285%2F8%29x%2B5 to our first plot to get:

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%285%2F8%29x-5%2C%285%2F8%29x%2B5%29+ Graph of y=%285%2F8%29x-5(red) and y=%285%2F8%29x%2B5(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.