SOLUTION: State whether the system is consistent and independent, consistent and dependent, or inconsistent: 4x+2y=8,2x+y=1

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Question 111719: State whether the system is consistent and independent, consistent and dependent, or inconsistent: 4x+2y=8,2x+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%2B2y=8

2x%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%2B2y=8 Start with the given equation



2y=8-4x Subtract 4+x from both sides



2y=-4x%2B8 Rearrange the equation



y=%28-4x%2B8%29%2F%282%29 Divide both sides by 2



y=%28-4%2F2%29x%2B%288%29%2F%282%29 Break up the fraction



y=-2x%2B4 Reduce



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




So let's solve for y on the second equation


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



1y=1-2x Subtract 2+x from both sides



1y=-2x%2B1 Rearrange the equation



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



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



y=-2x%2B1 Reduce





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


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-2x%2B4%2C-2x%2B1%29+ Graph of y=-2x%2B4(red) and y=-2x%2B1(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.