8x – py + 7 = 0; 4x – 2y + 3 = 0

(ii) 8x – py + 7 = 0; 4x – 2y + 3 = 0

Sol. 8x – py + 7 = 0

∴  8x – py = – 7

Comparing with a1x + b1y = c1 we get, a1 = 8, b1 = – p, c1 = – 7

4x – 2y + 3 = 0

∴  4x – 2y = – 3

Comparing with a2x + b2y = c2 we get, a2 = 4, b2 = – 2, c2 = – 3

a₁/a₂ = 8/4 = 2  ............ eq. no. (i)

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

c₁/c₂ = -7/-3 = 7/3   ............ eq. no. (iii)

We know that the condition for the equations to have unique solution is_

a₁/a₂ ≠ b₁/b₂

∴ 2 ≠ p/2

∴ p ≠ 4

∴ The simultaneous equations will have unique solution for all values of p except 4.