SOLUTION: solve the systems of equations using graphs. [a].2x+3y=-1 [b].3x+4y=0

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Question 762445: solve the systems of equations using graphs.
[a].2x+3y=-1
[b].3x+4y=0
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

[a] 2x%2B3y=-1
[b] 3x%2B4y=0

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



Start with the given system of equations:


2x%2B3y=-1

3x%2B4y=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


2x%2B3y=-1 Start with the given equation



3y=-1-2x Subtract 2+x from both sides



3y=-2x-1 Rearrange the equation



y=%28-2x-1%29%2F%283%29 Divide both sides by 3



y=%28-2%2F3%29x%2B%28-1%29%2F%283%29 Break up the fraction



y=%28-2%2F3%29x-1%2F3 Reduce



Now lets graph y=%28-2%2F3%29x-1%2F3 (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+%28-2%2F3%29x-1%2F3%29+ Graph of y=%28-2%2F3%29x-1%2F3




So let's solve for y on the second equation


3x%2B4y=0 Start with the given equation



4y=0-3x Subtract 3+x from both sides



4y=-3x%2B0 Rearrange the equation



y=%28-3x%2B0%29%2F%284%29 Divide both sides by 4



y=%28-3%2F4%29x%2B%280%29%2F%284%29 Break up the fraction



y=%28-3%2F4%29x%2B0 Reduce





Now lets add the graph of y=%28-3%2F4%29x%2B0 to our first plot to get:


Graph of y=%28-2%2F3%29x-1%2F3(red) and y=%28-3%2F4%29x%2B0(green)


From the graph, we can see that the two lines intersect at the point (4,-3) (note: you might have to adjust the window to see the intersection)