Linear Equations (C10)

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

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