4x + y = 7; 16x + ky = 28

(i) 4x + y = 7; 16x + ky = 28

Sol. 4x + y = 7

Comparing with a1x + b1y = c1 we get, a1 = 4, b1 = 1, c1 = 7

16x + ky = 28

Comparing with a2x + b2y = c2 we get, a2 = 16, b2 = k, c2 = 28

a₁/a₂ = 4/16 = ¼  ............ eq. no. (i)

b₁/b₂ = 1/k = 1/k ............ eq. no. (ii)

c₁/c₂ = 7/28 = ¼  ............ eq. no. (iii)

∵ The simultaneous equations have infinitely many solutions.

a₁/a₂ = b₁/b₂ = c₁/c₂

∴ ¼ = 1/k = ¼

∴ ¼ = 1/k

∴ k = 4