When solving linear equations what does ${0x_n = 0}$ mean? What if the system is used to find Nash equilibrium?

Question

When solving systems of linear equations one sometimes gets result like ${0x_n = 0}$ what does it mean for solving the system? Is it error on part of the solver or just feature of the assignment?

Edit: To extend the question. What would such result mean when looking for Nash equilibrium?

Answer 1

What values of $x_n$ satisfy the equation $0x_n=0$?

Answer: all of them. It is just an equation which happens to have infinitely many solutions.

This equation, in other words, does not limit the value of $x_n$ in any way. It doesn't provide a constraint that must be satisfied in the system.

Answer 2

$0x_n=0$ is the identity $0=0 \quad \forall x_n$ so it means that the equation is verified for all values of $x_n$.