How to solve equations with possible values for variables?

I'm working in a simulation project, and there is a step that I'd like to solve using MATLAB. I'll explain a very simplified system, but still similar to the one in the project. It goes as following: I have a set of 3 variables, and 4 conditions:

a1*4 + a2*3 + a3*1 = 6

a1 can be only 1 or 0

a2 can be only 1 or 0

a3 can be only 1 or 0

So, based on those restrictions, the only possible solution would be a1 = 1, a2 = 0, a3 = 1. How can I write this in matlab, and get this answer?

Thanks!

Answer 1

[Joshua]

This is not a very elegant solution, but it works.

clear
clc
syms a1 a2 a3
f=symfun(4*a1+3*a2+2*a3,[a1,a2,a3])

for i=0:1
    for j=0:1
        for k=0:1
            if f(i,j,k)==6
                answers=[i,j,k]
                break;
            end
        end
    end
end

if isempty(answers)==true
    error('No solution found')
end