What's the solution to this system of equation? $$
xy^3z^3 = yx^3z^3 = zx^3y^3
$$
Is there a way to solve this system?
I think the answer is 1, but i can't verify my intuition.

Clearly if one of the variables is $0$ then all three equations are satisfied. Suppose then that's not the case. We rewrite as
$$y^2 = x^2,\ \ x^2 = z^2,\ \ y^2 = z^2$$
Letting $x$ be a free-variable, we have
$y = \pm x$ and $z=\pm x$.
