### How to solve system of equations in polynomial ring over GF with a different variables

I want to reduce system of symbolyc equations by modulo.

I create field and polynomical ring

```
F = GF(31)
R.<x, y, z> = PolynomialRing(F)
```

And try to create system:

```
system = [
x == 3 * y,
z
```~~= ~~== 2 * x
]

To use `solve(system, [x, y, z])`

(here I expected solution `x = 3 * y`

, `z = 6 * y`

). But all of equations evaluate to False.

How to create correct equatiations?