I'm trying to solve the following system of linear equations derived from a transitional matrix for a regular Markov chain. I can't use matrix methods since that would involve finding the inverse of a non-square matrix, and I'm not clear on how the elimination method would work with this. Any ideas?

$$-0.25x + 0.15y + 0.05z = 0$$
$$0.05x - 0.25y + 0.1z = 0$$
$$0.2x + 0.1y - 0.15z = 0$$ 
$$x + y + z = 1$$

The solution is $x = 0.25, y = 0.25, z = 0.5$.