# Using SageMath to solve Simultaneous equations in a Boolean Ring

I'm trying to get SageMath to solve a system of equations in a Boolean Ring. Here is my code.

```
P.<x,y,z> = BooleanPolynomialRing(3, order= 'lex')
equations = [1+x+y+z, x+y, x*y+1, x+y]
zeros = [0,0,0,0]
```

I know that there are equation solvers for Sage, but I do not know how to have the answers of the equation be only in the Boolean Ring (ie. only 1 or 0). Obviously I can solve the equation by hand, but that's not the point here. Is there a way to have SageMath only output 0 or 1 as the answer?