SOLUTION: what is the value of (x - y) if 3x-5y=5 and x ----- =5/7 ? x+y

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Question 694485: what is the value of (x - y) if
3x-5y=5 and
x
----- =5/7 ?
x+y
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
You have the system
system%283x-5y=5%2Cx%2F%28x%2By%29=5%2F7%29 and the problem asks for the value of %28x-y%29

x%2F%28x%2By%29=5%2F7 --> 7%28x%2By%29x%2F%28x%2By%29=7%28x%2By%295%2F7 --> 7x=5%28x%2By%29 --> 7x=5x%2B5y%29 --> 7x-5x-5y=5x%2B5y-5x-5y%29 --> 2x-5y=0%29
Now we can re-write the system as
system%283x-5y=5%2C2x-5y=0%29

We can solve that system for x and y by elimination.
Subtracting the second equation from the first, we get
3x-5y-%282x-5y%29=5-0 --> 3x-5y-2x%2B5y=5 --> x=5
We can then substitute that value for x in one of the equations with x and y to find y.
Using 2x-5y=0, we get 2%2A5-5y=0 --> 10-5y=0 --> 10-5y%2B5y=0%2B5y --> 10=5y --> 10%2F5=5y%2F5 --> y=2

Substituting the valued found for x and y, we get
x-y=5-2 --> highlight%28x-y-3%29