SOLUTION: Solve the systems of equations by graphing. Then classify the system as consistent or inconsistent and the equations as dependent or independent y=-x-9 5x-4y=-27

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Question 145825: Solve the systems of equations by graphing. Then classify the system as consistent or inconsistent and the equations as dependent or independent
y=-x-9
5x-4y=-27
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Notice how the first equation is already in y form

So lets graph y=-x-9 (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+-x-9%29+ Graph of y=-x-9



So let's solve for y on the second equation

5x-4y=-27 Start with the given equation


-4y=-27-5x Subtract 5+x from both sides


-4y=-5x-27 Rearrange the equation


y=%28-5x-27%29%2F%28-4%29 Divide both sides by -4


y=%28-5%2F-4%29x%2B%28-27%29%2F%28-4%29 Break up the fraction


y=%285%2F4%29x%2B27%2F4 Reduce



Now lets add the graph of y=%285%2F4%29x%2B27%2F4 to our first plot to get:

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-x-9%2C%285%2F4%29x%2B27%2F4%29+ Graph of y=-x-9(red) and y=%285%2F4%29x%2B27%2F4(green)

From the graph, we can see that the two lines intersect at the point (-7,-2)

So this means that the system is consistent and independent.