SOLUTION: If 5x-6y = -123 and 3x + 13y = -107, what is the value of x and y?

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Question 198232: If 5x-6y = -123 and 3x + 13y = -107, what is the value of x and y?
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%285x-6y=-123%2C3x%2B13y=-107%29


3%285x-6y%29=3%28-123%29 Multiply the both sides of the first equation by 3.


15x-18y=-369 Distribute and multiply.


-5%283x%2B13y%29=-5%28-107%29 Multiply the both sides of the second equation by -5.


-15x-65y=535 Distribute and multiply.


So we have the new system of equations:
system%2815x-18y=-369%2C-15x-65y=535%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:


%2815x-18y%29%2B%28-15x-65y%29=%28-369%29%2B%28535%29


%2815x%2B-15x%29%2B%28-18y%2B-65y%29=-369%2B535 Group like terms.


0x%2B-83y=166 Combine like terms.


-83y=166 Simplify.


y=%28166%29%2F%28-83%29 Divide both sides by -83 to isolate y.


y=-2 Reduce.


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15x-18y=-369 Now go back to the first equation.


15x-18%28-2%29=-369 Plug in y=-2.


15x%2B36=-369 Multiply.


15x=-369-36 Subtract 36 from both sides.


15x=-405 Combine like terms on the right side.


x=%28-405%29%2F%2815%29 Divide both sides by 15 to isolate x.


x=-27 Reduce.


So the solutions are x=-27 and y=-2.


Which form the ordered pair .


This means that the system is consistent and independent.