SOLUTION: Sole the system of equations by graphing. Then classify the system as consistent or inconsistent and the equations as dependent or independent 3x-y=26 3x+4y=-14

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Question 145841: Sole the system of equations by graphing. Then classify the system as consistent or inconsistent and the equations as dependent or independent

3x-y=26
3x+4y=-14
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=26
3x%2B4y=-14




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=26 Start with the given equation


-y=26-3x Subtract 3+x from both sides


-y=-3x%2B26 Rearrange the equation


y=%28-3x%2B26%29%2F%28-1%29 Divide both sides by -1


y=%28-3%2F-1%29x%2B%2826%29%2F%28-1%29 Break up the fraction


y=3x-26 Reduce


Now lets graph y=3x-26 (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-26%29+ Graph of y=3x-26



So let's solve for y on the second equation

3x%2B4y=-14 Start with the given equation


4y=-14-3x Subtract 3+x from both sides


4y=-3x-14 Rearrange the equation


y=%28-3x-14%29%2F%284%29 Divide both sides by 4


y=%28-3%2F4%29x%2B%28-14%29%2F%284%29 Break up the fraction


y=%28-3%2F4%29x-7%2F2 Reduce



Now lets add the graph of y=%28-3%2F4%29x-7%2F2 to our first plot to get:

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+3x-26%2C%28-3%2F4%29x-7%2F2%29+ Graph of y=3x-26(red) and y=%28-3%2F4%29x-7%2F2(green)

From the graph, we can see that the two lines intersect at the point (6,-8)

So the system is consistent and independent