How to combine different equations automatically

Question

I have 9 different equations that contain only 7 unknowns. I would like to generate a code that creates all the possible systems of 7 equations and return the cases in which all the variables have a positive result. The 9 equations are:

    eq1 = 14*x+7*z-21.71
    eq2 = 15*x+11*z+w-38.55
    eq3=12*x+8*y+12*z+w-52.92
    eq4=12*x+8*y+14*z+t-61.7
    eq5=13*x+8*y+15*z+t-69.37
    eq6=4*x+17*y+14*r+s-98.32
    eq7=4*x+18*y+12*w+s-130.91
    eq8=4*x+18*y+15*w+2*t-165.45
    eq9=4*x+18*y+12*w+2*s-168.16

Answer 1

Adapted from this answer

What you want to do is iterate through all the combinations that only have 7 equations. You can do this with nested loops but it will get very ugly as you will have 7 nests.

itertools library in python (standard library) has a built in method for looping like this, so if you create a list of equations, you can iterate through all unique systems by doing the following

import itertools
eq = [eq1,eq2eq3,eq4,eq5,eq6,eq7,eq8,eq9]

for system in itertools.combinations(eq, 7):
    # do stuff to solve equations however you want

system is going to be a tuple containing the 7 equations in the system. From there use whatever solving technique you want to solve them and determine if all outputs are positive (i.e. numpy and matrix equations)