SOLUTION: Solve the following system of equations by graphing -3x-2y=0 3x-y=18

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Question 1002880: Solve the following system of equations by graphing
-3x-2y=0
3x-y=18

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

-3x-2y=0
3x-y=18
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Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


-3x-2y=0

3x-y=18





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


-3x-2y=0 Start with the given equation



-2y=0%2B3x Add 3+x to both sides



-2y=%2B3x%2B0 Rearrange the equation



y=%28%2B3x%2B0%29%2F%28-2%29 Divide both sides by -2



y=%28%2B3%2F-2%29x%2B%280%29%2F%28-2%29 Break up the fraction



y=%28-3%2F2%29x%2B0 Reduce



Now lets graph y=%28-3%2F2%29x%2B0 (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+%28-3%2F2%29x%2B0%29+ Graph of y=%28-3%2F2%29x%2B0




So let's solve for y on the second equation


3x-y=18 Start with the given equation



-y=18-3x Subtract 3+x from both sides



-y=-3x%2B18 Rearrange the equation



y=%28-3x%2B18%29%2F%28-1%29 Divide both sides by -1



y=%28-3%2F-1%29x%2B%2818%29%2F%28-1%29 Break up the fraction



y=3x-18 Reduce





Now lets add the graph of y=3x-18 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%28-3%2F2%29x%2B0%2C3x-18%29+ Graph of y=%28-3%2F2%29x%2B0(red) and y=3x-18(green)


From the graph, we can see that the two lines intersect at the point (4,-6) (note: you might have to adjust the window to see the intersection)