SOLUTION: solve the system by graphing 3x+2y=10 5x-3y=4

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Question 758525: solve the system by graphing
3x+2y=10
5x-3y=4

Answer by MathLover1(20850) 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%2B2y=10

5x-3y=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


3x%2B2y=10 Start with the given equation



2y=10-3x Subtract 3+x from both sides



2y=-3x%2B10 Rearrange the equation



y=%28-3x%2B10%29%2F%282%29 Divide both sides by 2



y=%28-3%2F2%29x%2B%2810%29%2F%282%29 Break up the fraction



y=%28-3%2F2%29x%2B5 Reduce



Now lets graph y=%28-3%2F2%29x%2B5 (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+%28-3%2F2%29x%2B5%29+ Graph of y=%28-3%2F2%29x%2B5




So let's solve for y on the second equation


5x-3y=4 Start with the given equation



-3y=4-5x Subtract 5+x from both sides



-3y=-5x%2B4 Rearrange the equation



y=%28-5x%2B4%29%2F%28-3%29 Divide both sides by -3



y=%28-5%2F-3%29x%2B%284%29%2F%28-3%29 Break up the fraction



y=%285%2F3%29x-4%2F3 Reduce





Now lets add the graph of y=%285%2F3%29x-4%2F3 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%28-3%2F2%29x%2B5%2C%285%2F3%29x-4%2F3%29+ Graph of y=%28-3%2F2%29x%2B5(red) and y=%285%2F3%29x-4%2F3(green)


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