Question

Find the value of k for which the given equations have infinitely many solution.

kx + 3y = 8; 6x + 9y = 24.​

Answer 1

Answer:

Equations are kx + 3y = 8 ; 6x + 9y = 24

OR

kx + 3y - 8 = 0 ; 6x + 9y - 24 = 0

a1 = k ; b1 = 3 ; c1 = -8

a2 = 6 ; b2 = 9 ; c2 = -24

a1/a2 = k/6

b1/b2 = 3/9 = 1/3

c1/c2 = -8/-24 = 8/24 = 1/3

Then condition for infinitely many solution is:

a1/a2 = b1/b2 = c1/c2

k/6 = 1/3

3 × k = 6 × 1

3k = 6

k = 6/3 = 2

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