Question

Find the value of k for which the pair of linear equation kx + Y = K(k) and X + KY = 1 have infinitely many solutions.

Answer 1

Given : The pair of linear equation...

kx + y = k² and x + ky = 1

To find : The value of k for which the pair of equations habe infinitely many solutions.

solution : we know, a₁x + b₁y = c₁ and a₂x + a₂y = c₂ are two equations...

condition of infinitely many solutions is...

a₁/a₂ = b₁/b₂ = c₁/c₂

here kx + y = k² and x + ky = 1 are two equations.

for infinitely many solutions,

k/1 = 1/k = k²/1

⇒k = 1/k

⇒k² = 1

⇒k = ± 1 ......(1)

also k/1 = k²/1

⇒k(k - 1) = 0

⇒k = 0, 1 ........(2)

get common solution of equations (1) and (2),

k = 1

Therefore the value of k = 1 for which the pair of equations have infinitely many solutions.