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Simultaneous Settlement (Posted on 2012-01-27) Difficulty: 3 of 5
Without solving for x and y, determine all possible values of x*y in this simultaneous equation:

x+x*y = 8 and, y+x*y = 9

Note: Solving for 1/x, 1/y, -x or -y is similarly NOT allowed.

No Solution Yet Submitted by K Sengupta    
Rating: 5.0000 (1 votes)

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Hints/Tips Hint | Comment 5 of 8 |
Well done Jer, broll and Dustin.

I know of only two methods of solving this, and Jer's solution comes closest to the second one.

The rules do allow for substitutions for x and y, which is not synonymous with solving for  x and y- but an extra credit goes to Dustin for bypassing these substitutions.

My second method involves multiplying the two equations together and solving for x*y using only the substitution for x+y (which as I mentioned earlier is very close to Jer's solution.)

My first method bypasses substitutions for x and y, and let this be an extra challenge to the readers.

Hint (Spoiler):

It uses the substitutions for x+y and x-y 

Edited on January 28, 2012, 12:31 am
  Posted by K Sengupta on 2012-01-28 00:21:49

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