All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
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)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Solution | Comment 1 of 8
Let xy = a so also y = a/x
Substitute into the first equation gives x + a = 8 then rewrite this  as x = 8 - a
Substitute into the second equation gives a/x + a = 9 then solve for x gives x = a/(9-a)

Substitute now for each x:
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

  Posted by Jer on 2012-01-27 11:10:40
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information