SOLUTION: Solve using the addition method. 3x-11y=9, -9x +33y=-27

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Question 192095: Solve using the addition method. 3x-11y=9, -9x +33y=-27
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-11y=9%2C-9x%2B33y=-27%29


3%283x-11y%29=3%289%29 Multiply the both sides of the first equation by 3.


9x-33y=27 Distribute and multiply.


So we have the new system of equations:
system%289x-33y=27%2C-9x%2B33y=-27%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-33y%29%2B%28-9x%2B33y%29=%2827%29%2B%28-27%29


%289x%2B-9x%29%2B%28-33y%2B33y%29=27%2B-27 Group like terms.


0x%2B0y=0 Combine like terms. Notice how the x and y terms cancel out.


0=0Simplify.


Since 0=0 is always true, this means that there are an infinite number of solutions. So the system is consistent and dependent.