Question

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

Options

• coincident

• parallel

• intersecting exactly at one point

• perpendicular to each other

Answer 1

Coincident

Explanation:

The equations are 5x – 15y – 8 = 0 and 15x – 45y – 24 = 0.

∴ `(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`

⇒ `(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.