Question

The graphs of the equations $5x-15y-8=0$ and $3x-9y-\frac{24}{5}=0$ are two lines which are

• A. Coincide
• B. Parallel
• C. Intersecting exactly at one point
• D. Perpendicular to each other

Answer 1

The correct option is A Coincide

Given , $5x-15y-8=0$ ..(1) and $3x-9y-\frac{24}{5}=0$ ..(2)

Let $a_{1}x+b_{1}y+c_1=0$ and $a_{2}x+b_{2}y+c_2=0$ represent coincident lines if $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

Here,$\frac{a_1}{a_2}=\frac{5}{3}$ , $\frac{b_1}{b_2}=\frac{-15}{-9}=\frac{5}{3}$ , $\frac{c_1}{c_2}=\frac{-8\times 5}{-24}=\frac{5}{3}$

Here $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

So they represent coincident lines.