SOLUTION: Solve the system of equations by graphing. Then classify the system as consistent or inconsistent and the equations as dependent or independent. x+y=7 x-y=-3

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Question 145838: Solve the system of equations by graphing. Then classify the system as consistent or inconsistent and the equations as dependent or independent.

x+y=7
x-y=-3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!


Start with the given system of equations:

x%2By=7
x-y=-3




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

x%2By=7 Start with the given equation


y=7-x Subtract +x from both sides


y=-x%2B7 Rearrange the equation




Now lets graph y=-x%2B7 (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%2B7%29+ Graph of y=-x%2B7



So let's solve for y on the second equation

x-y=-3 Start with the given equation


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


-y=-x-3 Rearrange the equation


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


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


y=x%2B3 Reduce



Now lets add the graph of y=x%2B3 to our first plot to get:

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-x%2B7%2Cx%2B3%29+ Graph of y=-x%2B7(red) and y=x%2B3(green)

From the graph, we can see that the two lines intersect at the point (2,5)

So the system is consistent and independent