SOLUTION: Solve the system: 2x+3y=5 3x-2y=-4

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Question 476489: Solve the system: 2x+3y=5 3x-2y=-4
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

2x%2B3y=5
3x-2y=-4

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



Start with the given system of equations:


2x%2B3y=5

3x-2y=-4





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=5 Start with the given equation



3y=5-2x Subtract 2+x from both sides



3y=-2x%2B5 Rearrange the equation



y=%28-2x%2B5%29%2F%283%29 Divide both sides by 3



y=%28-2%2F3%29x%2B%285%29%2F%283%29 Break up the fraction



y=%28-2%2F3%29x%2B5%2F3 Reduce



Now lets graph y=%28-2%2F3%29x%2B5%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%2B5%2F3%29+ Graph of y=%28-2%2F3%29x%2B5%2F3




So let's solve for y on the second equation


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



-2y=-4-3x Subtract 3+x from both sides



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



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



y=%28-3%2F-2%29x%2B%28-4%29%2F%28-2%29 Break up the fraction



y=%283%2F2%29x%2B2 Reduce





Now lets add the graph of y=%283%2F2%29x%2B2 to our first plot to get:


Graph of y=%28-2%2F3%29x%2B5%2F3(red) and y=%283%2F2%29x%2B2(green)


From the graph, we can see that the two lines intersect at the point (-2%2F13,23%2F13) (note: you might have to adjust the window to see the intersection)