Question

Find the value(s) of k for which the pair of linear equations kx + y = k2 and x + ky = 1 have infinitely many solutions. 10.

Answer 1

Here, a1/a2= k/1, b1/b2=1/k, c1/c2= k2/1
for infinite solution, we have
a1/a2=b1/b2=c1/c2
from 1st n 2nd terms
k/1=1/k
k2=1
k=1
from 2nd n 3rd terms
1/k=k2/1
k2=k
k2-k=0
k(k-1)=0
k-1=0
k=1

Answer 2

Answer:

Step-by-step explanation:

Given Equation are

Kx + y - k² = 0    ..... (i)

x + ky - 1 = 0 .....(ii)

Since (i) and (ii) have infinitely many solutions.

⇒ k/1 = 1/k = - k²/- 1

They are 1st = 2nd = 3rd

From 1st and 2nd = k/1 = 1/k

⇒ k² = 1

⇒ k = ± 1 .... (iii)

From 2nd and 3rd = 1/k = k²/1

⇒ k³ = 1

⇒ k = 1 ....(iv)

From (iii) and (iv), we get

⇒ k = 1

Hence, the value of k is 1.