SOLUTION: I need to classify the system as consistent or inconsistent, and dependent or independent. x + y = 8 x-y=4

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Question 737500: I need to classify the system as consistent or inconsistent, and dependent or independent.
x + y = 8
x-y=4
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


1x%2By=8

1x-y=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


1x%2By=8 Start with the given equation



1y=8-x Subtract +x from both sides



1y=-x%2B8 Rearrange the equation



y=%28-x%2B8%29%2F%281%29 Divide both sides by 1



y=%28-1%2F1%29x%2B%288%29%2F%281%29 Break up the fraction



y=-x%2B8 Reduce



Now lets graph y=-x%2B8 (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%2B8%29+ Graph of y=-x%2B8




So let's solve for y on the second equation


1x-y=4 Start with the given equation



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



-y=-x%2B4 Rearrange the equation



y=%28-x%2B4%29%2F%28-1%29 Divide both sides by -1



y=%28-1%2F-1%29x%2B%284%29%2F%28-1%29 Break up the fraction



y=x-4 Reduce





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%2B8%2Cx-4%29+ Graph of y=-x%2B8(red) and y=x-4(green)


From the graph, we can see that the two lines intersect at the point (6,2) (note: you might have to adjust the window to see the intersection)



we usually use the word "consistent" when we are more interested in
indicating that the system does HAVE a solution, rather than
indicating how many solutions it has
"Inconsistent" means no solution,
"Independent" and "Dependent" BOTH mean there is a solution
since your system has solution (one intersection point), it is "Independent" or "Dependent"