(i) 3x + y = 10; 9x + py = 23
Sol. 3x + y = 10
Comparing
with a1x
+ b1y
= c1 we
get, a1 =
3, b1 =
1, c1 =
10
9x
+ py = 23
Comparing
with a2x
+ b2y
= c2 we
get, a2 =
9, b2 =
p, c2 =
23
a1/a2
= 3/9 = 1/3 ............ eq. no. (i)
b1/b2
= 1/p ............ eq. no. (ii)
c1/c2
= 10/23 ............ eq. no. (iii)
We know
that the condition for the
equations to have unique solution is_
a1/a2
≠ b1/b2
∴ 1/3
≠ 1/p
∴ p ≠
3
∴ The
simultaneous equations will have unique solution for all values of p except 3.
