SOLUTION: I have one more question. Solve the system of equations by graphing. Then classify the system as consistent or inconsistent, and the equation as dependent or independent. 5x - y

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: I have one more question. Solve the system of equations by graphing. Then classify the system as consistent or inconsistent, and the equation as dependent or independent. 5x - y      Log On


   

Question 144155: I have one more question.
Solve the system of equations by graphing. Then classify the system as consistent or inconsistent, and the equation as dependent or independent.
5x - y = 25
5x + 6y = -10
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!


Start with the given system of equations:

5x-y=25
5x%2B6y=-10




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-y=25 Start with the given equation


-y=25-5x Subtract 5+x from both sides


-y=-5x%2B25 Rearrange the equation


y=%28-5x%2B25%29%2F%28-1%29 Divide both sides by -1


y=%28-5%2F-1%29x%2B%2825%29%2F%28-1%29 Break up the fraction


y=5x-25 Reduce


Now lets graph y=5x-25 (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+5x-25%29+ Graph of y=5x-25



So let's solve for y on the second equation

5x%2B6y=-10 Start with the given equation


6y=-10-5x Subtract 5+x from both sides


6y=-5x-10 Rearrange the equation


y=%28-5x-10%29%2F%286%29 Divide both sides by 6


y=%28-5%2F6%29x%2B%28-10%29%2F%286%29 Break up the fraction


y=%28-5%2F6%29x-5%2F3 Reduce



Now lets add the graph of y=%28-5%2F6%29x-5%2F3 to our first plot to get:

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+5x-25%2C%28-5%2F6%29x-5%2F3%29+ Graph of y=5x-25(red) and y=%28-5%2F6%29x-5%2F3(green)

From the graph, we can see that the two lines intersect at the point (4,-5). Since the two graphs intersect each other at one point, this means that the system is consistent and independent.