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March 13th, 2014, 12:50 PM   #1
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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)


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March 13th, 2014, 07:58 PM   #2
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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.
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March 13th, 2014, 10:17 PM   #3
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Re: Non-linear systems of equations

1)







I think that's all but it's getting late here . . . goodnight!
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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 canít both be 0.)
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