# Solving for variables in a series of nonlinear equations [closed]

I have a nonlinear expression in five variables. I want to use Mathematica to solve for three of the variables. I have a series of points giving values of x an y and I am trying to solve for a,b, and c.

I am having trouble in finding how to solve this. Does anyone know a Mathematica function that can do it? Or do I need to write some type of script to do this?

My expression is

$$(660 (-0.37 + b) (x - c))/(660 + a) - 0.37 c = y$$

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## closed as too localized by belisarius, Artes, Yves Klett, Silvia, Oleksandr R.May 15 '13 at 11:54

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Syntax for this would be Solve[{(660 (-0.37 + b) (x - c))/(660 + a) - 0.37 c == y,...}, {a,b,c}]. Note use of "==" (doubles equal sign) in the equation; a single one denoted Mathematica's Set which is not what you would want there. –  Daniel Lichtblau May 14 '13 at 23:30
@Daniel, Thank you very much, I'm very new to this program and still trying to learn and did not even know about the double =. So following that script, how would I input my x,y values for the expression? –  GuestRiverside229 May 14 '13 at 23:42
If you have three linearly independent points giving x and y values, you can use the Solve function to get a solution. If you have more than three, then you will need to fit a solution with one of Mathematica's functions for fitting data to a set of parameters. Which is your situation? –  m_goldberg May 15 '13 at 2:56

One way to find the parameters {a,b,c} is the following:

f[x_]=(660 (-0.37 + b) (x - c))/(660 + a) - 0.37 c
sol = FindFit[data, f[x], {a, b, c}, x]


Where data is a List[] of {x,y} pairs that you want to use to fit the parameters. The problem isn't very well posed however: f[x] describes a straight line with three parameters instead of the two that would be sufficient. The result is that your solution {a,b,c} will flail about wildly, trying to accomodate what is probably non-relevant variations in the data.

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You could rewrite the equation using two parameters d and e, to get it in the form of f[x_]= d x + e and fit that. d and e can be found using CoefficientList[(660 (-0.37 + b) (x - c))/(660 + a) - 0.37 c, x]. After finding d and e from the fit you can solve for a, b and c. –  Sjoerd C. de Vries May 15 '13 at 8:34
@SjoerdCdeVries Wouldn't that be underdetermined? –  SEngstrom May 15 '13 at 13:45
It is. You'd have a free parameter. –  Sjoerd C. de Vries May 15 '13 at 18:32