# 3 Equations with 2 Unknowns

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## Main Question or Discussion Point

I have 3 equations with two unknowns of the form:

$$r_i == f_i (g,\beta)$$

Where g and $\beta$ are the independent unknown variables and $r_i$ are known experimentally, but have some error associated with them, say something like $4.3 \pm 0.3$ and there are other errors associated with constants inside the $f_i$.

My question is how do I solve for the objectively "best" fit to those two parameters. I remember doing something like this back in prob/stats, I believe I do something like a $\chi^2$ fit but I can't find anything online about it that doesn't concern bins of data points, but rather continuous functions. (Or do I have to simulate data, then fit it)

Can anyone lead me in the right direction? I don't have any of my undergrad books with me.

The equations are all something like :
$$r_1 =\frac{\left(g^2 x+g^2y-\frac{\beta }{3}\right)^2}{g^2 }$$
with some variations on the form. So nothing with unsolvable functions.

EDIT: Oh and I plan on using Mathematica to do this, but I'd rather understand the mathematics first.

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Stephen Tashi