Consider the homogeneous system given by
ax + by = 0
cx + dy = 0
(a) Show that if (x0, y0) is a solution to this linear system, then so is (kx0, ky0) for any constant k.
(b) Show that if (x0, y0) and (x1, y1) are solutions to this linear system, then so is (x0 + x1, y0 + y1).