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

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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