SOLUTION: Solve this system of equations by graphing: x – 2y = 8 3x – 2y = 12

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Question 127777: Solve this system of equations 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!


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)