Question

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

Answer 1

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

We have:

a1/a2 = k/1

b1/b2 = 1/k

c1/c2 = k2/1

For infinitely many solutions,

a1/a2 = b1/b2 = c1/c2

k/1 = 1/k

k2 = 1

k = 1, -1 ... (i)

1/k = k2/1

k3 = 1

k = 1 ... (ii)

From (i) and (ii),

k = 1

Answer 2

multiply second eq by k and then subtract it by eq 1 then by solving both the equations you get k= 1,-1