SOLUTION: 5x+5y=-13, 7x-3y=11 using the elimination method solve this please.

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Question 309872: 5x+5y=-13, 7x-3y=11 using the elimination method solve this please.
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%2B5y=-13%2C7x-3y=11%29


3%285x%2B5y%29=3%28-13%29 Multiply the both sides of the first equation by 3.


15x%2B15y=-39 Distribute and multiply.


5%287x-3y%29=5%2811%29 Multiply the both sides of the second equation by 5.


35x-15y=55 Distribute and multiply.


So we have the new system of equations:
system%2815x%2B15y=-39%2C35x-15y=55%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%2B15y%29%2B%2835x-15y%29=%28-39%29%2B%2855%29


%2815x%2B35x%29%2B%2815y%2B-15y%29=-39%2B55 Group like terms.


50x%2B0y=16 Combine like terms.


50x=16 Simplify.


x=%2816%29%2F%2850%29 Divide both sides by 50 to isolate x.


x=8%2F25 Reduce.


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15x%2B15y=-39 Now go back to the first equation.


15%288%2F25%29%2B15y=-39 Plug in x=8%2F25.


24%2F5%2B15y=-39 Multiply.


5%2824%2Fcross%285%29%2B15y%29=5%28-39%29 Multiply both sides by the LCD 5 to clear any fractions.


24%2B75y=-195 Distribute and multiply.


75y=-195-24 Subtract 24 from both sides.


75y=-219 Combine like terms on the right side.


y=%28-219%29%2F%2875%29 Divide both sides by 75 to isolate y.


y=-73%2F25 Reduce.


So the solutions are x=8%2F25 and y=-73%2F25.


Which form the ordered pair .


This means that the system is consistent and independent.