SOLUTION: State whether the system is consistent and independent, consistent and dependent, or inconsistent; x+y=4 2x-y=-7

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Question 111720: State whether the system is consistent and independent, consistent and dependent, or inconsistent; x+y=4 2x-y=-7
Answer by jim_thompson5910(35256) 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=4

2x-y=-7





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=4 Start with the given equation



1y=4-x Subtract +x from both sides



1y=-x%2B4 Rearrange the equation



y=%28-x%2B4%29%2F%281%29 Divide both sides by 1



y=%28-1%2F1%29x%2B%284%29%2F%281%29 Break up the fraction



y=-x%2B4 Reduce



Now lets graph y=-x%2B4 (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%2B4%29+ Graph of y=-x%2B4




So let's solve for y on the second equation


2x-y=-7 Start with the given equation



-y=-7-2x Subtract 2+x from both sides



-y=-2x-7 Rearrange the equation



y=%28-2x-7%29%2F%28-1%29 Divide both sides by -1



y=%28-2%2F-1%29x%2B%28-7%29%2F%28-1%29 Break up the fraction



y=2x%2B7 Reduce





Now lets add the graph of y=2x%2B7 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-x%2B4%2C2x%2B7%29+ Graph of y=-x%2B4(red) and y=2x%2B7(green)


From the graph, we can see that the two lines intersect at the point (-1,5) (note: you might have to adjust the window to see the intersection)


Since a solution exists, and it's unique, the system is consistent and independent