Solving Linear-Quadratic Systems by Substitution

The sphere $x^2 + y^2 + z^2 = 1$ has many rational solutions. For instance, start with the point $(x,y,z) = (1,0,0)$, and draw the line $\{x = 1-t, y = t, z = t\}$ through it to get another intersection with the sphere, $(x,y,z) = (a,b,c)$. What is $300a+30b+3c$?