Consider system of equations $x(x-y)(x-z)=3$, $y(y-x)(y-z)=3$, $z(z-y)=3$ where $x,y,z\in\mathbb C$. Then which of the following is/are True?
A. There are different solutions.
B. sum $(x+y+z)$ in any solution is Zero.
C. No two of $x,y,z$ can be simultaneously real
D. Any solution lies on a straight line.
I tried various ways but I couldn't figure it out. According to Wolfram Alpha, there are $7$ different solutions to it.