Question

If the lines 3x + 2 ky = 2 and 2x + 5y + 1 = 0 are parallel, then find value of k.

Answer 1

The Given pair of  linear equation is :

3x +2ky = 2
3x +2ky -2= 0………(1)

2x +5y+1= 0………….(2)

On comparing with General form of a pair of linear equations  in two variables x & y is: a1x + b1y + c1 = 0
and   a2x+b2y + c2= 0

a1= 3, b1= 2k, c= -2
a2= 2 , b2= 5, c= 1

a1/a2= 3/2 ,  b1/b2= 2k/5 & c1/c2= -2/1

Given: A pair of linear equations will represent  Parallel Lines, i.e has no Solution, if

a1/a2 = b1/b2 ≠c1/c2
3/2 = 2k/5 ≠ -2/1

(I)      (II)        (III)

on taking I & II terms
3/2 = 2k/5
3× 5 = 2k × 2
15 = 4k
k = 15/4

Hence, the value of k = 15/4

HOPE THIS WILL HELP YOU...