SOLUTION: Solve the systems of equations by graphing. Then classify the system as consistent or inconsistent and the equations as dependent or independent 3u+v=16 3u=v+26

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Question 145828: Solve the systems of equations by graphing. Then classify the system as consistent or inconsistent and the equations as dependent or independent

3u+v=16
3u=v+26
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
note: I'm replacing "u" with "x" and "v" with "y" so I can graph the equations.


Start with the given system of equations:

3x%2By=16
3x=y%2B26




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%2By=16 Start with the given equation


y=16-3x Subtract 3+x from both sides


y=-3x%2B16 Rearrange the equation




Now lets graph y=-3x%2B16 (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%2B16%29+ Graph of y=-3x%2B16



So let's solve for y on the second equation

3x=y%2B26 Start with the given equation


3x-26=y Subtract 26 from both sides


y=3x-26 Rearrange the equation



Now lets add the graph of y=3x-26 to our first plot to get:

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-3x%2B16%2C3x-26%29+ Graph of y=-3x%2B16(red) and y=3x-26(green)

From the graph, we can see that the two lines intersect at the point (7,-5)


So this means that the system is consistent and independent.