In a city map drawn on a Cartesian grid, Road X is known to pass through the intersections (0,0) and (3,6). Another Road Y is reported to pass through (0,0) and (5,10).
(a) Determine the equations of Road X and Road Y.
(b) Decide whether Road X and Road Y are truly two different roads or actually the same road represented twice. Give complete reasoning based on their common points and the theorem regarding the intersection of lines.