SOLUTION: Solve the system by graphing: 4x+4y=4 x+y=1

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Question 82881: Solve the system by graphing:
4x+4y=4
x+y=1
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:


4x%2B4y=4

1x%2By=1





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


4x%2B4y=4 Start with the given equation



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



4y=-4x%2B4 Rearrange the equation



y=%28-4x%2B4%29%2F%284%29 Divide both sides by 4



y=%28-4%2F4%29x%2B%284%29%2F%284%29 Break up the fraction



y=-x%2B1 Reduce



Now lets graph y=-x%2B1 (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%2B1%29+ Graph of y=-x%2B1




So let's solve for y on the second equation


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



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



1y=-x%2B1 Rearrange the equation



y=%28-x%2B1%29%2F%281%29 Divide both sides by 1



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



y=-x%2B1 Reduce





Now lets add the graph of y=-x%2B1 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-x%2B1%2C-x%2B1%29+ Graph of y=-x%2B1(red) and y=-x%2B1(green)


From the graph, we can see that the two lines are identical (one lies perfectly on top of the other) and intersect at all points of both lines. So there are an infinite number of solutions and the system is dependent.