SOLUTION: solve the system by the elimination method 5x+5y=11 7x-3y=17

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Question 146609: solve the system by the elimination method
5x+5y=11
7x-3y=17
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=11%2C7x-3y=17%29


3%285x%2B5y%29=3%2811%29 Multiply the both sides of the first equation by 3.


15x%2B15y=33 Distribute and multiply.


5%287x-3y%29=5%2817%29 Multiply the both sides of the second equation by 5.


35x-15y=85 Distribute and multiply.


So we have the new system of equations:
system%2815x%2B15y=33%2C35x-15y=85%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=%2833%29%2B%2885%29


%2815x%2B35x%29%2B%2815y%2B-15y%29=33%2B85 Group like terms.


50x%2B0y=118 Combine like terms. Notice how the y terms cancel out.


50x=118 Simplify.


x=%28118%29%2F%2850%29 Divide both sides by 50 to isolate x.


x=59%2F25 Reduce.


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15x%2B15y=33 Now go back to the first equation.


15%2859%2F25%29%2B15y=33 Plug in x=59%2F25.


177%2F5%2B15y=33 Multiply.


5%28177%2Fcross%285%29%2B15y%29=5%2833%29 Multiply both sides by the LCD 5 to clear any fractions.


177%2B75y=165 Distribute and multiply.


75y=165-177 Subtract 177 from both sides.


75y=-12 Combine like terms on the right side.


y=%28-12%29%2F%2875%29 Divide both sides by 75 to isolate y.


y=-4%2F25 Reduce.


So our answer is x=59%2F25 and y=-4%2F25.


Which form the ordered pair .


This means that the two equations are consistent and independent.