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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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Some Thoughts No Subject | Comment 3 of 8 |
It seems you've both solved for x or y.

Jer, you have x = 8 - a, broll, you have y=x+1.

It's my understanding this is against the rules.  It seems easy enough to work around the rules, though.  Here's Jer's solution with a small modification.

"Let xy = a so also y = a/x
Substitute into the first equation gives x + a = 8 then rewrite this as x +1 = 8 - a +1
Substitute into the second equation gives a/x + a = 9 then solve for x +1 gives x +1 = a/(9-a) +1

Substitute now for each x +1: (the rest of the solution follows exactly)
8 - a +1= a/(9-a) +1
8 - a = a/(9-a)
72 - 17a + a^2 = a
a^2 - 18a + 72 = 0
this quadratic has solutions
a= 6 or a=12

so the possible values of x*y are 6 and 12"

I don't know if this is allowed.  We're not allowed to solve for x, are we allowed to solve for x+1?

Edited on January 27, 2012, 5:57 pm

Edited on January 27, 2012, 5:59 pm
  Posted by Dustin on 2012-01-27 17:54:57

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