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Q about Nonlinear Simul. Eq


Hello,

I'm a newbie in this group.  I have a question about solving nonlinear
simultaneous equation.  Please forgive me if my question is trivial.

Is there any built-in function solving nonlinear simultaneous equations 
in Mathematica?  Or do I have to make a subroutine or a function to do 
that?  
  
Currently I'm using Mathematica v. 2.2.3 under UNIX.  


The following shows a small example for your reference:

I tried to estimate x and y from this equation:
*********************************************************************
NSolve[{
        x - 4 (Exp[-1 - 2x] / (Exp[-1 - 2x] + Exp[-2 - y])) == 0, 
        y - 4 (Exp[-2 -  y] / (Exp[-1 - 2x] + Exp[-2 - y])) == 0, 
        x + y                                               == 4
        }, 
        {x, y}]
*********************************************************************

After hitting shift+enter, what I get is the following message and the 
output:

*********************************************************************
Solve::tdep: 
   The equations appear to involve transcendental functions of
     the variables in an essentially non-algebraic way.

Out[1]=
               -1 - 2 x
           -4 E
NSolve[{------------------- + x == 0, 
         -1 - 2 x    -2 - y
        E         + E
 
           -2 - y
       -4 E
   ------------------- + y == 0, x + y == 4}, {x, y}]
    -1 - 2 x    -2 - y
   E         + E
********************************************************************

Thank you for your help in advance.


J.C.

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