Question

If the lines given by 3x + 2ky = 2 and 2x + 5y + 1 = 0 are not parallel, then k has to be ______.

पर्याय

• `15/4`

• `≠15/4`

• any rational number

• any rational number having 4 as denominator

Answer 1

If the lines given by 3x + 2ky = 2 and 2x + 5y + 1 = 0 are not parallel, then k has to be `underlinebb(≠15/4)`.

Explanation:

Line 1: 3x + 2ky = 2

Line 2: 2x + 5y + 1 = 0

Condition for not being parallel:

Two lines are parallel when their slopes are equal.

Two lines are not parallel when their slopes are not equal.

Slope of Line 1:

General form = Ax + By + C = 0

Slope = `-A/B`

Rewrite:

3x + 2ky − 2 = 0

So slope m₁ = `-3/(2k)`

Slope of Line 2:

2x + 5y + 1 = 0

Slope m₂ = `-2/5`

Condition for not parallel:

m₁ ≠ m₂

`-3/(2k) ≠ -2/5`

Remove minus signs:

`3/(2k) ≠ 2/5`

Cross multiply:

15 ≠ 4k

So, `k ≠ 15/4`