(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.
