SOLUTION: 3x-5y=-3,-9x-15y=9 how do you solve using the elimination method?

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Question 244750: 3x-5y=-3,-9x-15y=9 how do you solve using the elimination method?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:
system%283x-5y=-3%2C-9x-15y=9%29


3%283x-5y%29=3%28-3%29 Multiply the both sides of the first equation by 3.


9x-15y=-9 Distribute and multiply.


So we have the new system of equations:
system%289x-15y=-9%2C-9x-15y=9%29


Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%289x-15y%29%2B%28-9x-15y%29=%28-9%29%2B%289%29


%289x%2B-9x%29%2B%28-15y%2B-15y%29=-9%2B9 Group like terms.


0x%2B-30y=0 Combine like terms.


-30y=0 Simplify.


y=%280%29%2F%28-30%29 Divide both sides by -30 to isolate y.


y=0 Reduce.


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9x-15y=-9 Now go back to the first equation.


9x-15%280%29=-9 Plug in y=0.


9x=-9 Multiply.


x=%28-9%29%2F%289%29 Divide both sides by 9 to isolate x.


x=-1 Reduce.


So the solutions are x=-1 and y=0.


Which form the ordered pair .


This means that the system is consistent and independent.


Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer.


Graph of 3x-5y=-3 (red) and -9x-15y=9 (green)