SOLUTION: Solve the systems of equations by graphing. Then classify the systems as consistant or inconsistant and as dependant or independant. 8x-6y=36 6y-8x=-36

Algebra ->  Equations -> SOLUTION: Solve the systems of equations by graphing. Then classify the systems as consistant or inconsistant and as dependant or independant. 8x-6y=36 6y-8x=-36      Log On


   

Question 146610: Solve the systems of equations by graphing. Then classify the systems as consistant or inconsistant and as dependant or independant.
8x-6y=36
6y-8x=-36
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:

8x-6y=36
6y-8x=-36








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

8x-6y=36 Start with the given equation


-6y=36-8x Subtract 8+x from both sides


-6y=-8x%2B36 Rearrange the equation


y=%28-8x%2B36%29%2F%28-6%29 Divide both sides by -6


y=%28-8%2F-6%29x%2B%2836%29%2F%28-6%29 Break up the fraction


y=%284%2F3%29x-6 Reduce


Now lets graph y=%284%2F3%29x-6 (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+%284%2F3%29x-6%29+ Graph of y=%284%2F3%29x-6



6y-8x=-36 Start with the second equation.


6y=-36%2B8x Add 8x to both sides.


y=%28-36%2B8x%29%2F%286%29 Divide both sides by 6 to isolate y.



y=%284%2F3%29x-6 Break up the fraction and rearrange the terms




Now lets add the graph of y=%283%2F4%29x%2B9%2F2 to our first plot to get:

+graph%28+600%2C+600%2C+-10%2C+20%2C+-10%2C+20%2C+%284%2F3%29x-6%2C%284%2F3%29x-6%29+ Graph of y=%284%2F3%29x-6(red) and y=%284%2F3%29x-6(green)

From the graph, we can see that the two lines are the same. So there are an infinite number of solutions


So the system is consistent and dependent.