SOLUTION: Solve the system of equations by graphing. Then classify the system as consistent or inconsistent or inconsistent and the equations as dependent or independent. 2x-6y=42 3x-9x=-

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Solve the system of equations by graphing. Then classify the system as consistent or inconsistent or inconsistent and the equations as dependent or independent. 2x-6y=42 3x-9x=-      Log On


   

Question 146408: Solve the system of equations by graphing. Then classify the system as consistent or inconsistent or inconsistent and the equations as dependent or independent.
2x-6y=42
3x-9x=-21
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!


Start with the given system of equations:

2x-6y=42
3x-9y=-21




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-6y=42 Start with the given equation


-6y=42-2x Subtract 2+x from both sides


-6y=-2x%2B42 Rearrange the equation


y=%28-2x%2B42%29%2F%28-6%29 Divide both sides by -6


y=%28-2%2F-6%29x%2B%2842%29%2F%28-6%29 Break up the fraction


y=%281%2F3%29x-7 Reduce


Now lets graph y=%281%2F3%29x-7 (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+%281%2F3%29x-7%29+ Graph of y=%281%2F3%29x-7



So let's solve for y on the second equation

3x-9y=-21 Start with the given equation


-9y=-21-3x Subtract 3+x from both sides


-9y=-3x-21 Rearrange the equation


y=%28-3x-21%29%2F%28-9%29 Divide both sides by -9


y=%28-3%2F-9%29x%2B%28-21%29%2F%28-9%29 Break up the fraction


y=%281%2F3%29x%2B7%2F3 Reduce



Now lets add the graph of y=%281%2F3%29x%2B7%2F3 to our first plot to get:

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%281%2F3%29x-7%2C%281%2F3%29x%2B7%2F3%29+ Graph of y=%281%2F3%29x-7(red) and y=%281%2F3%29x%2B7%2F3(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.