SOLUTION: which ordered pair is a solution to hte system 3x+2y=-9 and 5x-3y=4

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Question 655332: which ordered pair is a solution to hte system 3x+2y=-9 and 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=-9

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=-9 Start with the given equation



2y=-9-3x Subtract 3+x from both sides



2y=-3x-9 Rearrange the equation



y=%28-3x-9%29%2F%282%29 Divide both sides by 2



y=%28-3%2F2%29x%2B%28-9%29%2F%282%29 Break up the fraction



y=%28-3%2F2%29x-9%2F2 Reduce



Now lets graph y=%28-3%2F2%29x-9%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+%28-3%2F2%29x-9%2F2%29+ Graph of y=%28-3%2F2%29x-9%2F2




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 of y=%28-3%2F2%29x-9%2F2(red) and y=%285%2F3%29x-4%2F3(green)


From the graph, we can see that the two lines intersect at the point (-1,-3) (note: you might have to adjust the window to see the intersection)