Question

For what value of k, do the equations 3x – y + 8 = 0 and 6x – ky = –16 represent
coincident lines?
(A) 1/2 (B) – 1/ 2 (C) 2 (D) –2

NCERT Class X
Mathematics - Exemplar Problems

Chapter _PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

Answer 1

As per the equations, 3x – y + 8 = 0

6x – ky = –16

a1=3, b1=-1, c1=8

a2=6, b2=-k, c2=16

a1/a2 = 3/6 = ½

b1/b2 = -1/-k = 1/k

c1/c2 = 8/16 = ½

if a1/a2 = b1/b2 = c1/c2

then two lines will be coincident

½ = 1/k = ½  

=> 1/k = 1/2 => k=2