If the lines 2x + 3y = 6 and 6x-ky 18 are coincident lines, then find the value of k.
Answers
Answer:
for line to be coincident k = -9
Given : lines 2x + 3y = 6 and 6x-ky = 18 are coincident lines
To Find : the 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)
2x + 3y = 6
6x-ky = 18
a₁/a₂ = b₁/b₂ = c₁/c₂ coincident lines
=> 2/6 = 3/-k = 6/18
=> 1/3 = 3/-k = 1/3
=> k = - 9
value of k is - 9
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