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