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?