SOLUTION: 5x+3y=-11 7x-2y=13

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Question 554869: 5x+3y=-11
7x-2y=13
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%2B3y=-11%2C7x-2y=13%29


2%285x%2B3y%29=2%28-11%29 Multiply the both sides of the first equation by 2.


10x%2B6y=-22 Distribute and multiply.


3%287x-2y%29=3%2813%29 Multiply the both sides of the second equation by 3.


21x-6y=39 Distribute and multiply.


So we have the new system of equations:
system%2810x%2B6y=-22%2C21x-6y=39%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:


%2810x%2B6y%29%2B%2821x-6y%29=%28-22%29%2B%2839%29


%2810x%2B21x%29%2B%286y%2B-6y%29=-22%2B39 Group like terms.


31x%2B0y=17 Combine like terms.


31x=17 Simplify.


x=%2817%29%2F%2831%29 Divide both sides by 31 to isolate x.


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10x%2B6y=-22 Now go back to the first equation.


10%2817%2F31%29%2B6y=-22 Plug in x=17%2F31.


170%2F31%2B6y=-22 Multiply.


31%28170%2Fcross%2831%29%2B6y%29=31%28-22%29 Multiply both sides by the LCD 31 to clear any fractions.


170%2B186y=-682 Distribute and multiply.


186y=-682-170 Subtract 170 from both sides.


186y=-852 Combine like terms on the right side.


y=%28-852%29%2F%28186%29 Divide both sides by 186 to isolate y.


y=-142%2F31 Reduce.


So the solutions are x=17%2F31 and y=-142%2F31.


Which form the ordered pair .


This means that the system is consistent and independent.


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Jim