Question

The value of k for which the pair of equations 3x + 2y + 5 = 0 and kx - 4y - 10 = 0 has infinitely many solution is :

a) 6
b) -6
c) 4
d) -4​

Answer 1

Answer:

I think c is the right answer

Answer 2

Given: Equations 3x + 2y + 5 = 0 and kx - 4y - 10 = 0 has infinitely many 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)

3x + 2y + 5 = 0

kx - 4y - 10 = 0

infinitely many solution

Hence  3/k  =  2/-4  = 5/-10

=> 3/k  = -1/2

=> k = - 6

Value of k is - 6

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