SOLUTION: Solve each of the following by graphing x+2y=4 x-y=1

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Question 107766: Solve each of the following by graphing
x+2y=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:


1x%2B2y=4

1x-y=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


1x%2B2y=4 Start with the given equation



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



2y=-x%2B4 Rearrange the equation



y=%28-x%2B4%29%2F%282%29 Divide both sides by 2



y=%28-1%2F2%29x%2B%284%29%2F%282%29 Break up the fraction



y=%28-1%2F2%29x%2B2 Reduce



Now lets graph y=%28-1%2F2%29x%2B2 (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%2B2%29+ Graph of y=%28-1%2F2%29x%2B2




So let's solve for y on the second equation


1x-y=1 Start with the given equation



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



-y=-x%2B1 Rearrange the equation



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



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



y=x-1 Reduce





Now lets add the graph of y=x-1 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%28-1%2F2%29x%2B2%2Cx-1%29+ Graph of y=%28-1%2F2%29x%2B2(red) and y=x-1(green)


From the graph, we can see that the two lines intersect at the point (2,1) (note: you might have to adjust the window to see the intersection)