Question

For what value of k, the pair of linear equations 4x + ky +6 = 0 and
2x + 2y +2 = 0 does not have a solution​

Answer 1

Given :  the pair of linear equations 4x + ky +6 = 0 and

2x + 2y +2 = 0 does not have a solution​

To Find : Value of K

Solution:

Pair of linear equations

a₁x  +  b₁y + c₁  =  0

a₂x  +  b₂y + c₂  =  0

Consistent

if a₁/a₂ ≠ b₁/b₂   (unique solution  and lines intersects each others)

  a₁/a₂ = b₁/b₂ = c₁/c₂   (infinite solutions and line coincide each other )

Inconsistent

if  a₁/a₂ = b₁/b₂ ≠  c₁/c₂  ( No solution , lines are parallel to each other)

4x + ky +6 = 0  

2x + 2y +2 = 0

does not have a solution​

=>  a₁/a₂ = b₁/b₂ ≠  c₁/c₂

=> 4/2   = k/2   ≠  6/2

=> 2 = k/2    ≠ 3

=> 4 = k ≠  6

Hence value of k = 4

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