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.

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