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=6 x+y=-4

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Question 145840: Solve the system of equations by graphing. Then classify the system as consistent or inconsistent and the equations as dependent or independent,

x+y=6
x+y=-4
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=6
x%2By=-4




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=6 Start with the given equation


y=6-x Subtract +x from both sides


y=-x%2B6 Rearrange the equation




Now lets graph y=-x%2B6 (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%2B6%29+ Graph of y=-x%2B6



So let's solve for y on the second equation

x%2By=-4 Start with the given equation


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


y=-x-4 Rearrange the equation

Now lets add the graph of y=-x-4 to our first plot to get:

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-x%2B6%2C-x-4%29+ Graph of y=-x%2B6(red) and y=-x-4(green)

From the graph, we can see that the two lines are parallel and will never intersect. So there are no solutions and the system is inconsistent.