SOLUTION: Solve the following by graphing: x-2y=8 3x-2y=12

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Question 82038: Solve the following by graphing:
x-2y=8
3x-2y=12
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-2y=8

3x-2y=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


1x-2y=8 Start with the given equation



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



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



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



y=%28-1%2F-2%29x%2B%288%29%2F%28-2%29 Break up the fraction



y=%281%2F2%29x-4 Reduce



Now lets graph y=%281%2F2%29x-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+%281%2F2%29x-4%29+ Graph of y=%281%2F2%29x-4




So let's solve for y on the second equation


3x-2y=12 Start with the given equation



-2y=12-3x Subtract 3+x from both sides



-2y=-3x%2B12 Rearrange the equation



y=%28-3x%2B12%29%2F%28-2%29 Divide both sides by -2



y=%28-3%2F-2%29x%2B%2812%29%2F%28-2%29 Break up the fraction



y=%283%2F2%29x-6 Reduce





Now lets add the graph of y=%283%2F2%29x-6 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%281%2F2%29x-4%2C%283%2F2%29x-6%29+ Graph of y=%281%2F2%29x-4(red) and y=%283%2F2%29x-6(green)


From the graph, we can see that the two lines intersect at the point (2,-3) (note: you might have to adjust the window to see the intersection)