Question: Solve maple function

I want to solve a system of algebraic equations in maple using as follows:

equations:={b[1](2)*a[1](2, 1) = 1/2, b[1](2)*a[1](2, 1)^2 = 1/3, b[1](2)*a[2](2, 1) = 1/2, b[1](2)*a[2](2, 1)^2 = 1/3, b[2](2)*a[1](2, 1) = 1/2, b[2](2)*a[2](2, 1) = 1/2, b[1](2)*(a[3](2, 1)+a[3](2, 2))*a[1](2, 1) = 1/3, b[1](2)*(a[3](2, 1)+a[3](2, 2))*a[2](2, 1) = 1/3, b[1](2)*a[2](2, 1)*a[1](2, 1) = 1/3, b[1](1)*(a[3](1, 1)+a[3](1, 2))+b[1](2)*(a[3](2, 1)+a[3](2, 2)) = 1/2, b[1](1)*(a[3](1, 1)+a[3](1, 2))^2+b[1](2)*(a[3](2, 1)+a[3](2, 2))^2 = 1/3, b[2](1)*(a[3](1, 1)+a[3](1, 2))+b[2](2)*(a[3](2, 1)+a[3](2, 2)) = 1/2, b[1](1)+b[1](2) = 1, b[2](1)+b[2](2) = 1}

variables:={a[1](2, 1), a[2](2, 1), a[3](1, 1), a[3](1, 2), a[3](2, 1), a[3](2, 2), b[1](1), b[1](2), b[2](1), b[2](2), b[3](1), b[3](2)}

solve(equations,variables);

But I get an error mesage that the equations is not valid equation or expression.

Any help?