The graphs of the equations `5x-15y = 8 and 3x-9y=24/5` are two line which are

Options

A. coincident
B. parallel
C. intersecting exactly at one point
D. perpendicular to each other

Answer

A

Explanation

The equations are ` 5x - 15 y - 8 = 0 and 15x - 45 y - 25 = 0`.
` therefore (a_1)/(a_2) = (5)/(15) = (1)/(3), (b_1)/(b_2) = (-15)/(-45) = (1)/(3) and (c_1)/(c_2) = (-8)/(-24) = (1)/(3)`
` rArr (a_1)/(a_2) = (b_1)/(b_2) = (c_1)/(c_2)` and therefore the system has infinitely many solutions.
Hence, the graph lines are coincident.