4y = kx – 10; 3x = 2y + 5

(ii) 4y = kx – 10; 3x = 2y + 5

Sol. 4y = kx – 10

∴  – kx + 4y = – 10

Comparing with a1x + b1y = c1 we get, a1 = – k, b1 = 4, c1 = – 10

3x = 2y + 5

∴  3x – 2y = 5

Comparing with a2x + b2y = c2 we get, a2 = 3, b2 = – 2, c2 = 5

a₁/a₂ = -k/3 = -k/3  ............ eq. no. (i)

b₁/b₂ = 4/-2 = -2 ............ eq. no. (ii)

c₁/c₂ = -10/5 = -2  ............ eq. no. (iii)

∵ The simultaneous equations have infinitely many solutions.

a₁/a₂ = b₁/b₂ = c₁/c₂

∴ -k/3 = -2 = -2

∴ -k/3 = -2

∴ - k  = - 6

∴ k = 6