Question

For what value of k system of given lines 3x + 2ky = 2 and 2x + 5y + 1 = 0 are i) parallel ii) intersecting iii) coincident

Answer 1

Step-by-step explanation:

Here,

3x + 2ky -2 = 0 ------------ (1)

2x + 5y + 1 =0 -------------(2)

from (1), a = 3 from (2), d = 2

b = 2k e = 5

c = -2 f = 1

i) parallel,

b/e ≠ c/f

Therefore,

b/e ≠ c/f

or, 2k/5 ≠ -2/1

or, 2k ≠ -10

or, k ≠ -5

Hence , the given system of lines parallel to each other for all real values of k, other than -5.

ii) intersecting ,

a/d ≠ b/e

Therefore,

a/d ≠ b/e

or,3/2 ≠ 2k/5

or, 15 ≠ 4k

or, 4k ≠ 15

Thus, k ≠ 15/4

Hence , the given system of lines parallel to each other for all real values of k, other than 15/4.

iii) coincident,

a/d = b/e = c/f

Therefore,

a/d = b/e

or,3/2 = 2k/5

or, 15 = 4k

or, 4k = 15

Thus, k = 15/4