@Carl Love 

Thank you this code is great! How can i filter the list so that it outputs only the solutions to a subset of the variables?

My problem is actually 11^3 equations in 11^2 variables but i only care about the possible solutions for 11 of those variables.

Essentailly i want the equivalence classes of solutions under the relation: that two different solution sets (of 11^2 variables) are the same if a specific subset of 11 solutions are the same.