Having 3 known positive variables (Z1,Z2,Z3) such that:
$$Z_1 = A+B+C+D+E$$ $$Z_2 = A+B+F-G$$ $$Z_3 = A-B-D+G$$
I want to obtain possible solutions (distributions) for {A,B,C...G} such that A,B,C... are all positive
I actually want to know a general way to do this, since my real problem involves more than 100 'letters' and tens of equations.
Is there anyway to do that? or any field that studies this?