SOLUTION: solve the system by graphing 3x + y = 6 3x - y = 0

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Question 92431: solve the system by graphing
3x + y = 6
3x - y = 0

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:


3x%2By=6

3x-y=0





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%2By=6 Start with the given equation



1y=6-3x Subtract 3+x from both sides



1y=-3x%2B6 Rearrange the equation



y=%28-3x%2B6%29%2F%281%29 Divide both sides by 1



y=%28-3%2F1%29x%2B%286%29%2F%281%29 Break up the fraction



y=-3x%2B6 Reduce



Now lets graph y=-3x%2B6 (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+-3x%2B6%29+ Graph of y=-3x%2B6




So let's solve for y on the second equation


3x-y=0 Start with the given equation



-y=0-3x Subtract 3+x from both sides



-y=-3x%2B0 Rearrange the equation



y=%28-3x%2B0%29%2F%28-1%29 Divide both sides by -1



y=%28-3%2F-1%29x%2B%280%29%2F%28-1%29 Break up the fraction



y=3x%2B0 Reduce





Now lets add the graph of y=3x%2B0 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-3x%2B6%2C3x%2B0%29+ Graph of y=-3x%2B6(red) and y=3x%2B0(green)


From the graph, we can see that the two lines intersect at the point (1,3) (note: you might have to adjust the window to see the intersection)