SOLUTION: y=2x-4 and x+2y=12 solve the system of linear equations by graphing

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Question 1100209: y=2x-4 and x+2y=12
solve the system of linear equations by graphing
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
y=2x-4 and x+2y=12
2x-y=4 and x+2y=12
Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


2x-y=4

1x%2B2y=12





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-y=4 Start with the given equation



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



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



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



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



y=2x-4 Reduce



Now lets graph y=2x-4 (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-4%29+ Graph of y=2x-4




So let's solve for y on the second equation


1x%2B2y=12 Start with the given equation



2y=12-x Subtract +x from both sides



2y=-x%2B12 Rearrange the equation



y=%28-x%2B12%29%2F%282%29 Divide both sides by 2



y=%28-1%2F2%29x%2B%2812%29%2F%282%29 Break up the fraction



y=%28-1%2F2%29x%2B6 Reduce





Now lets add the graph of y=%28-1%2F2%29x%2B6 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+2x-4%2C%28-1%2F2%29x%2B6%29+ Graph of y=2x-4(red) and y=%28-1%2F2%29x%2B6(green)


From the graph, we can see that the two lines intersect at the point (4,4) (note: you might have to adjust the window to see the intersection)