Math Is Fun Forum

abotaha

Member

Registered: 2010-07-18

Posts: 13

system of nonlinear equation

Hello guys,

I am not good in advance mathematics.
I have system of nonlinear equation and I want to solve it analytically, but I face some difficulties.
The system is :

where:

and

are constants.

any suggestion and help would be appreciated.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: system of nonlinear equation

Hi;

You can reduce the system down to solving for x in:

Once you have x, then you plug in to one of the equations to get y.

But you will see what a tremendous understatement the above is.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

abotaha

Member

Registered: 2010-07-18

Posts: 13

Re: system of nonlinear equation

Thanks for the answer. it helps a lot and i tried to solved it using cubic formula. I searched for the cubic formula  (http://en.wikipedia.org/wiki/Cubic_formula#General_formula_of_roots). I found that there are some restriction (limitation or may say conditions) that gives different solution which I really did not understand it.
could you explain to me little bit please or any suggestion about solution using cubic formula.

Last edited by abotaha (2010-07-23 08:24:10)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: system of nonlinear equation

Hi abotaha;

Did you try Cardano's method? Yes, you will have to make some slight assumptions on the coefficients but they are minor.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

abotaha

Member

Registered: 2010-07-18

Posts: 13

Re: system of nonlinear equation

It could be a good idea let me try and see if there is another method.

Thanks

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: system of nonlinear equation

Hi;

I always suggest using that horrible formula. It makes people a lot more receptive to doing this by computer.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: system of nonlinear equation

Hi;

These haven't been tested in battle yet...

With:

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

abotaha

Member

Registered: 2010-07-18

Posts: 13

Re: system of nonlinear equation

oh, thanks a lot
you are amazing.
i'll consider these solution and i think to find root for y i have to substitute x value in one of the equation  in post #1.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: system of nonlinear equation

you are amazing.

I have a nice singing voice, but that's about it. In this case Mathematica is amazing.

Yes, once you have an x just substitute back into one of those to get y.

Check, check, check, I may have made a mistake copying!

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: system of nonlinear equation

I am curious how you transfered the answer from Mathematica to this post, bobbym.
Did you type it?

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X'(y-Xβ)=0

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: system of nonlinear equation

Hi George,Y;

No, my typing skills are worse than a monkey without a head. Mathematica can output in latex.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.