3x + y = 10; 9x + py = 23

(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.

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