(Q.19). Find the value of ‘k’ for which the pair of equations 2x – ky + 3 = 0, 4x + 6y – 5 = 0 represent parallel lines.

Given: 2x – ky + 3 = 0

4x + 6y – 5 = 0

If the above lines are to be parallel, then

a1
a2
 =
b1
b2
 ≠
c1
c2
i.e.,
=
-
 ≠
-
⇒
2
4
 =
-k
6
 ⇒ k =
- ×
= -

∴ k = – is the required value for which lines are .