March 13th, 2014, 12:50 PM  #1 
Newbie Joined: Oct 2013 Posts: 29 Thanks: 1  Nonlinear systems of equations
Hello, I'm having a really tough time solving the following nonlinear 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: 7,663 Thanks: 2643 Math Focus: Mainly analysis and algebra  Re: Nonlinear 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: 7,943 Thanks: 1134 Math Focus: Elementary mathematics and beyond  Re: Nonlinear systems of equations
1) I think that's all but it's getting late here . . . goodnight! 
March 14th, 2014, 01:49 AM  #4  
Member Joined: Mar 2013 Posts: 90 Thanks: 0  Re: Nonlinear systems of equations Quote:
Suppose . Then If , exists, giving , an absurdity. Hence one of must be 0. (Note though that implies they can’t both be 0.)  

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