SOLUTION: Where do 2x-3y=6 and 4x+3y=12 intersect on the graph and what does the graph look like?

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Question 712543: Where do 2x-3y=6 and 4x+3y=12 intersect on the graph and what does the graph look like?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

2x-3y=6 and 4x%2B3y=12

Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


2x-3y=6

4x%2B3y=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-3y=6 Start with the given equation



-3y=6-2x Subtract 2+x from both sides



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



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



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



y=%282%2F3%29x-2 Reduce



Now lets graph y=%282%2F3%29x-2 (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+%282%2F3%29x-2%29+ Graph of y=%282%2F3%29x-2




So let's solve for y on the second equation


4x%2B3y=12 Start with the given equation



3y=12-4x Subtract 4+x from both sides



3y=-4x%2B12 Rearrange the equation



y=%28-4x%2B12%29%2F%283%29 Divide both sides by 3



y=%28-4%2F3%29x%2B%2812%29%2F%283%29 Break up the fraction



y=%28-4%2F3%29x%2B4 Reduce





Now lets add the graph of y=%28-4%2F3%29x%2B4 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%282%2F3%29x-2%2C%28-4%2F3%29x%2B4%29+ Graph of y=%282%2F3%29x-2(red) and y=%28-4%2F3%29x%2B4(green)


From the graph, we can see that the two lines intersect at the point (3,0) (note: you might have to adjust the window to see the intersection)