SOLUTION: Could you help solve: 8/x-5/y=51/14 6/x+(-10)/y=-(29/7)

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Question 151299: Could you help solve:
8/x-5/y=51/14 6/x+(-10)/y=-(29/7)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
8%2Fx-5%2Fy=51%2F14 Start with the first equation.


14xy%288%2Fcross%28x%29-5%2Fcross%28y%29%29=14xy%2851%2Fcross%2814%29%29 Multiply both sides by 14xy. This will eliminate the fractions.


112y-70x=51xy Distribute and multiply


-70x=51xy-112y Subtract 112y from both sides.


-70x=y%2851x-112%29 Factor out y from the right side.


%28-70x%29%2F%2851x-112%29=y Divide both sides by 51x-112.



So after isolating y of the first equation, we get y=%28-70x%29%2F%2851x-112%29



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6%2Fx%2B%28-10%29%2Fy=-%2829%2F7%29 Move onto the second equation


6%2Fx%2B%28-10%29%2F%28%28-70x%29%2F%2851x-112%29%29=-%2829%2F7%29 Plug in y=%28-70x%29%2F%2851x-112%29. In other words, replace "y" with %28-70x%29%2F%2851x-112%29


6%2Fx%2B%28-10%29%28%2851x-112%29%2F%28-70x%29%29=-%2829%2F7%29 Multiply the numerator "-10" by the reciprocal of the fraction in the denominator.


6%2Fx%2B%28-510x%2B1120%29%2F%28-70x%29=-%2829%2F7%29 Distribute


6%2Fx%2B%28510x-1120%29%2F%2870x%29=-%2829%2F7%29 Simplify.


Multiply both sides by 70x. This will eliminate the fractions.


420%2B510x-1120=-290x Simplify


420-1120=-290x-510x Subtract 510x from both sides.


-700=-800x Combine like terms.


%28-700%29%2F%28-800%29=x Divide both sides by -800.


x=7%2F8 Reduce. So this is the first part of the answer.


y=%28-70x%29%2F%2851x-112%29 Go back to the first isolated equation


y=%28-70%287%2F8%29%29%2F%2851%287%2F8%29-112%29 Plug in x=7%2F8


y=%28-245%2F4%29%2F%28357%2F8-112%29 Multiply and reduce


y=%28-245%2F4%29%2F%28-539%2F8%29 Subtract


y=%28-245%2F4%29%2A%288%2F%28-539%29%29 Multiply the first fraction by the reciprocal of the second fraction.


y=10%2F11 Multiply and reduce



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Answer:

So the answer is x=7%2F8 and y=10%2F11 which forms the ordered pair