how to figure the initial guess to optimize

I have the following problem to code using python:



I have 7 parameters: x,y,z,t, HF, M1F, and M2F. The user should input any of these 3 and the program should calculate the rest.



The relations that I have are:



HF = -xyt



M1F = -2xzt + 4yzt - xyt + 4tz^2



M2F = 2yzt - xyt



1 = -2xt + 2yt + 4zt



Attempt to solve the problem:



I have 7 parameters and the user should input 3 => I will be left with 4 parameters. So it's all about solving a system of 4 nonlinear equations with 4 unknowns.



I read online that scipy.optimize could be used to solve a system of nonlinear equations. But I need an initial guess.



Going back to the physics of the problem I have the following initial conditions:



x > 0



y > 0



z < 0



HF > 0



M1F > 0



M2F > 0



M2F > M1F (solving this inequality from the above equations I get: -x + y + 2z < 0)



HF > M1F + d (solving this inequality from the above equations I get: -x + 2y + 2z < 0)



How can these initial conditions help me get the initial guess so that I can solve my problem using scipy.optimize?