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.

Answer 1

According to question

Equations given

kx + y = k^2
and
x + ky = 1

Since the equations have infinitely many solutions
Thus
comparing the coefficients of x and y

k/1 = 1/k = 2k/1

thus
k = +1 or -1
k = +1/ root2 or -1/ root2

Answer 2

Answer: 1

Step-by-step explanation:

For pair of equations kx + 1y = k2 and 1x + ky  = 1

We have :

$\bf\huge\frac{a1}{a2} = \frac{k}{1},\frac{b1}{b2} = \frac{1}{k},\frac{c1}{c2} = \frac{k^{2} }{1}$

For infinitely many solutions,

$\bf\huge\frac{a1}{a2} = \frac{b1}{b2} = \frac{c1}{c2}$

$\bf\huge\frac{k1}{1} = \frac{1}{k}$

k^2 = 1

k = -1 , 1

$\bf\huge\frac{1}{k} = \frac{k^2}{1}$

k^3 = 1

⇒ k = 1