I know the conditions of being a basis. The vectors in set should be linearly independent and they should span the vector space.
So while finding a basis for the equation $y = z$, it's easy to see that the $x$ is free variable and if we call it as $x = s$, $y$ and $z$ becomes $t$ for example. And the basis are $(1,0,0)$ and $(0,1,1)$
However, i could not apply the same logic to $x - 2y + 5z =0$ Is there any free variable in this equation? How can I find the basis?