Solving system of 3 implicit equations

I am trying to solve a system of 3 implicit equations..

Trying to find alpha_1, beta and X1. The values of CMCm,CMC1, and CMC2 are known.

Any suggestions on how to approach towards a solution would be helpful thanks :)

Answer 1

[Torsten]

Rewriting equation (3) gives

d1 = x1 * exp(beta*(1-x1)^2) * CMC1/CMCm

This is almost equation (1).

If I assume that you made a mistake in the rearrangement, you have only 2 equations for 3 unknowns. This is not solvable in general.