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I'm looking for a numerical method to solve simultaneous polynomial equations that can be implemented in a computer program. I have included an example of a typical pair of equations that I may need to solve. In this case the two variables that I need to solve for are x and y, all other terms are known constants (with b equal to approximately 5).

Equation 1:

A1 * (k1 - x) * (k1 - 1 + x)^b + A2 * (k2 - y) * (k2 - 1 + y)^b = 0

Equation 2:

[b * (k1 - x)^2 + (k1 - 1 + x)^2] - [b * (k2 - y)^2 + (k2 - 1 + y)^2] = 0

It has been suggested that a Gaussian elimination method along with the Newton-Raphson method be used. Unfortunately, i have been scratching my head over this one for a couple of days now, but still have not found an answer.

Is anyone able to offer any thoughts/suggestions on this subject?

Thanks