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 March 13th, 2014, 12:50 PM #1 Newbie   Joined: Oct 2013 Posts: 29 Thanks: 1 Non-linear systems of equations Hello, I'm having a really tough time solving the following non-linear systems of equations. They are the equations that arose from the search for constraned extrema of multivariable functions. Any help would be greatly appreciated: 1) 2) March 13th, 2014, 07:58 PM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,690 Thanks: 2669 Math Focus: Mainly analysis and algebra Re: Non-linear systems of equations In 1) you can rearrange each of the first two equations to give you expressions for x and y in terms of z and only, You can then substitute those into the third equation. You then have an equation that expresses z in terms of only. Substituting that back into the first two equations will give you x and y, each in terms of only. And you can then substitute into the fourth equation to work out a value for . For 2) you can use the third equation directly in the first two, and from the results calculate . Except that, on first sight, that seems to give and . Are you sure that question is correct? If it is, then I conclude that either x or y is equal to zero, the other is therefore 1. March 13th, 2014, 10:17 PM #3 Global Moderator   Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,968 Thanks: 1152 Math Focus: Elementary mathematics and beyond Re: Non-linear systems of equations 1) I think that's all but it's getting late here . . . goodnight! March 14th, 2014, 01:49 AM   #4
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Re: Non-linear systems of equations

Quote:
 Originally Posted by Akcope 2)
If then . If then .

Suppose . Then

If , exists, giving , an absurdity. Hence one of must be 0. (Note though that implies they can�t both be 0.) Tags equations, nonlinear, systems Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Jake_88 Linear Algebra 1 June 15th, 2010 05:59 AM MathMCMC Advanced Statistics 0 February 11th, 2010 11:43 AM nchung1988 Algebra 4 February 7th, 2010 05:57 AM maxpalme Algebra 1 April 2nd, 2009 10:33 AM maxpalme Abstract Algebra 1 December 31st, 1969 04:00 PM

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