SOLUTION: solve the following systems of equations by graphing and find intersection point. 3x+6y=-9 4x-6y=16

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Question 739849: solve the following systems of equations by graphing and find intersection point. 3x+6y=-9
4x-6y=16
Found 2 solutions by MathLover1, lwsshak3:
Answer by MathLover1(20849) 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%2B6y=-9

4x-6y=16





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%2B6y=-9 Start with the given equation



6y=-9-3x Subtract 3+x from both sides



6y=-3x-9 Rearrange the equation



y=%28-3x-9%29%2F%286%29 Divide both sides by 6



y=%28-3%2F6%29x%2B%28-9%29%2F%286%29 Break up the fraction



y=%28-1%2F2%29x-3%2F2 Reduce



Now lets graph y=%28-1%2F2%29x-3%2F2 (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+%28-1%2F2%29x-3%2F2%29+ Graph of y=%28-1%2F2%29x-3%2F2




So let's solve for y on the second equation


4x-6y=16 Start with the given equation



-6y=16-4x Subtract 4+x from both sides



-6y=-4x%2B16 Rearrange the equation



y=%28-4x%2B16%29%2F%28-6%29 Divide both sides by -6



y=%28-4%2F-6%29x%2B%2816%29%2F%28-6%29 Break up the fraction



y=%282%2F3%29x-8%2F3 Reduce





Now lets add the graph of y=%282%2F3%29x-8%2F3 to our first plot to get:


Graph of y=%28-1%2F2%29x-3%2F2(red) and y=%282%2F3%29x-8%2F3(green)


From the graph, we can see that the two lines intersect at the point (1,-2) (note: you might have to adjust the window to see the intersection)

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
solve the following systems of equations by graphing and find intersection point. 3x+6y=-9
4x-6y=16
***
3x+6y=-9
4x-6y=16
add
7x=7
x=1
6y=4x-16
6y=4-16
6y=-12
y=-2
intersection point:(1,-2)
see graph below:

+graph%28+300%2C+300%2C+-5%2C+5%2C+-5%2C+5%2C+-x%2F2-3%2F2%2C2x%2F3-8%2F3%29+