The value of k for which the lines 5x+7y=3 and 15x + 21y = k coincide is :-
(a) 9
(b) 5
(c) 7
(d) 18
(Full answer by step by step needa)
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Given : 5x+7y=3 and 15x + 21y = k
To Find : Value of k for which these lines coincide
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)
5x+7y=3
15x + 21y = k
coincide
=> 5/15 = 7/21 = 3/k
=> 1/3 = 1/3 = 3/k
=> k = 9
Value of k is 9
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