SOLUTION: Solve the system by graphing. Then graphify the system consistant or inconsistant and as dependent or independent. 5x - 8y = -40 5y - 8x = 40 Will someone please help with

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Solve the system by graphing. Then graphify the system consistant or inconsistant and as dependent or independent. 5x - 8y = -40 5y - 8x = 40 Will someone please help with       Log On


   

Question 140987: Solve the system by graphing. Then graphify the system consistant or inconsistant and as dependent or independent.
5x - 8y = -40
5y - 8x = 40
Will someone please help with this one. It is independent right? And Consistant? Or am I totally wrong if so WHY????
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
5y+-+8x+=+40 Start with the second equation


-+8x+%2B+5y++=+40 Rearrange the terms






So we now have the system of equations:

5x-8y=-40
-8x%2B5y=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-40 Rearrange the equation


y=%28-5x-40%29%2F%28-8%29 Divide both sides by -8


y=%28-5%2F-8%29x%2B%28-40%29%2F%28-8%29 Break up the fraction


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


Now lets graph y=%285%2F8%29x%2B5 (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%2B5%29+ Graph of y=%285%2F8%29x%2B5



So let's solve for y on the second equation

-8x%2B5y=40 Start with the given equation


5y=40%2B8x Add 8+x to both sides


5y=%2B8x%2B40 Rearrange the equation


y=%28%2B8x%2B40%29%2F%285%29 Divide both sides by 5


y=%28%2B8%2F5%29x%2B%2840%29%2F%285%29 Break up the fraction


y=%288%2F5%29x%2B8 Reduce



Now lets add the graph of y=%288%2F5%29x%2B8 to our first plot to get:

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%285%2F8%29x%2B5%2C%288%2F5%29x%2B8%29+ Graph of y=%285%2F8%29x%2B5(red) and y=%288%2F5%29x%2B8(green)

With help from a graphing calculator, we can see that the two lines intersect at the point (-40%2F13,40%2F13)



This means that system is independent and consistent. So you are correct.