SOLUTION: Solve by the elimination method 5x+3y=-7 7x-2y=13

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Question 563666: Solve by the elimination method
5x+3y=-7
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=-7%2C7x-2y=13%29


2%285x%2B3y%29=2%28-7%29 Multiply the both sides of the first equation by 2.


10x%2B6y=-14 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=-14%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=%28-14%29%2B%2839%29


%2810x%2B21x%29%2B%286y%2B-6y%29=-14%2B39 Group like terms.


31x%2B0y=25 Combine like terms.


31x=25 Simplify.


x=%2825%29%2F%2831%29 Divide both sides by 31 to isolate x.


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10x%2B6y=-14 Now go back to the first equation.


10%2825%2F31%29%2B6y=-14 Plug in x=25%2F31.


250%2F31%2B6y=-14 Multiply.


31%28250%2Fcross%2831%29%2B6y%29=31%28-14%29 Multiply both sides by the LCD 31 to clear any fractions.


250%2B186y=-434 Distribute and multiply.


186y=-434-250 Subtract 250 from both sides.


186y=-684 Combine like terms on the right side.


y=%28-684%29%2F%28186%29 Divide both sides by 186 to isolate y.


y=-114%2F31 Reduce.


So the solutions are x=25%2F31 and y=-114%2F31.


Which form the ordered pair .


This means that the system is consistent and independent.
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