Question

If the lines given by 3x + 2ky = 2, 2x + 5y + 1 = 0 are parallel, then the value of k is
5/4
2/5
15/4
3/2

Answer 1

Answer:

lines are parallel, that means ratio cofficients of X and y is equal for both lines :-

so,

(3/2)= 2k / 5

so, k =15/4

Answer 2

Answer:

k = 15/4

Note:

★ If we consider two lines whose equations are ax + by + c = 0 and a'x + b'y + c' = 0 ;

Then ;

• They are intersecting if a/a' ≠ b/b'

• They are coincident if a/a' = b/b' = c/c'

• They are parallel if a/a' = b/b' = c/c'

Solution:

Here,

The given equations of lines are ;

3x + 2ky = 2

2x + 5y + 1 = 0

The given system of lines can be rewritten as ;

3x + 2ky - 2 = 0

2x + 5y + 1 = 0

Clearly,

a = 3

a' = 2

b = 2k

b' = 5

c = -2

c' = 1

Thus,

a/a' = 3/2

b/b' = 2k/5

c/c' = -2/1 = -2

For the given lines to be parallel ;

a/a' = b/b' ≠ c/c'

Thus,

3/2 = 2k/5 ≠ -2

Clearly,

3/2 ≠ -2

Thus,

The only condition for the given lines to be parallel is follow ↓

=> 3/2 = 2k/5

=> 2k/5 = 3/2

=> k = (3/2) × (5/2)

=> k = (3×5) / (2×2)

=> k = 15/4

Hence,

The required value of k is 15/4 .