(Q.20). For what value of ‘k’, the pair of equation 3x + 4y + 2 = 0 and 9x + 12y + k = 0 represent coincident lines.

Given: 3x + 4y + 2 = 0

9x + 12y + k = 0

If the lines are to be coincident with each other, then

a1
a2
 =
b1
b2
 =
c1
c2
i.e.,
=
=
⇒
1
 =
1
 =
k
 ⇒
1
 =
k

∴ k = × =