Question

The equations 2x - ky + 7 = 0 and 6x - 12y + 15 = 0 have no solution for
1. k = -4
2. k = 4
3. k = 1
4. k = -1

Answer 1

Correct Answer - Option 2 : k = 4

Concept: 

If two linear equations

a1​x + b1y ​= c1​ and a2​x + b2y ​= c2​. Then,

(a) If a1​​/a2 = b1​​/b2 ​​= c1​​/c2 ​​, the system is consistent and has infinitely many solutions.

(b) If a1​​/a2 = b1​​/b2 ≠ c1​​/c2 the system has no solution and is inconsistent

Calculation:

The equations 2x - ky + 7 = 0 and 6x - 12y + 15 = 0

2/6 = - k/-12 ≠ 7/15

Using, 2/6 = - k/-12

⇒ k =  24/6 =  4

∴ At k =  4, The equations 2x - ky + 7 = 0 and 6x - 12y + 15 = 0 have no solution