SOLUTION: Solve the system of equations by graphing. Then classify the system as consistent or inconsistent and the equations as dependent or independent. 3x-y=6 3x+4y=-9 I am so los

Algebra ->  Linear-equations -> SOLUTION: Solve the system of equations by graphing. Then classify the system as consistent or inconsistent and the equations as dependent or independent. 3x-y=6 3x+4y=-9 I am so los      Log On


   

Question 145808: Solve the system of equations by graphing. Then classify the system as consistent or inconsistent and the equations as dependent or independent.
3x-y=6
3x+4y=-9
I am so lost on how do this problem, please help!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:

3x-y=6
3x%2B4y=-9




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

3x-y=6 Start with the given equation


-y=6-3x Subtract 3+x from both sides


-y=-3x%2B6 Rearrange the equation


y=%28-3x%2B6%29%2F%28-1%29 Divide both sides by -1


y=%28-3%2F-1%29x%2B%286%29%2F%28-1%29 Break up the fraction


y=3x-6 Reduce


Now lets graph y=3x-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+3x-6%29+ Graph of y=3x-6



So let's solve for y on the second equation

3x%2B4y=-9 Start with the given equation


4y=-9-3x Subtract 3+x from both sides


4y=-3x-9 Rearrange the equation


y=%28-3x-9%29%2F%284%29 Divide both sides by 4


y=%28-3%2F4%29x%2B%28-9%29%2F%284%29 Break up the fraction


y=%28-3%2F4%29x-9%2F4 Reduce



Now lets add the graph of y=%28-3%2F4%29x-9%2F4 to our first plot to get:

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+3x-6%2C%28-3%2F4%29x-9%2F4%29+ Graph of y=3x-6(red) and y=%28-3%2F4%29x-9%2F4(green)

From the graph, we can see that the two lines intersect at the point (1,-3)


So the system is consistent and independent