SOLUTION: Solve the system by graphing. 2x + 4y = 2 x + 2y = 1 Again someone help me please.

Algebra ->  Graphs -> SOLUTION: Solve the system by graphing. 2x + 4y = 2 x + 2y = 1 Again someone help me please.      Log On


   

Question 104033: Solve the system by graphing.
2x + 4y = 2
x + 2y = 1
Again someone help me please.
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:


2x%2B4y=2

1x%2B2y=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


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



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



4y=-2x%2B2 Rearrange the equation



y=%28-2x%2B2%29%2F%284%29 Divide both sides by 4



y=%28-2%2F4%29x%2B%282%29%2F%284%29 Break up the fraction



y=%28-1%2F2%29x%2B1%2F2 Reduce



Now lets graph y=%28-1%2F2%29x%2B1%2F2 (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+%28-1%2F2%29x%2B1%2F2%29+ Graph of y=%28-1%2F2%29x%2B1%2F2




So let's solve for y on the second equation


1x%2B2y=1 Start with the given equation



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



2y=-x%2B1 Rearrange the equation



y=%28-x%2B1%29%2F%282%29 Divide both sides by 2



y=%28-1%2F2%29x%2B%281%29%2F%282%29 Break up the fraction



y=%28-1%2F2%29x%2B1%2F2 Reduce





Now lets add the graph of y=%28-1%2F2%29x%2B1%2F2 to our first plot to get:


Graph of y=%28-1%2F2%29x%2B1%2F2(red) and y=%28-1%2F2%29x%2B1%2F2(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.