4x + y = 7; 16x + ky = 28

(i) 4x + y = 7; 16x + ky = 28

Sol. 4x + y = 7
Comparing with a1x + b1y = c1 we get, a1 = 4, b1 = 1, c1 = 7

16x + ky = 28
Comparing with a2x + b2y = c2 we get, a2 = 16, b2 = k, c2 = 28

a1/a2 = 4/16 = ¼  ............ eq. no. (i)
b1/b2 = 1/k = 1/k ............ eq. no. (ii)
c1/c2 = 7/28 = ¼  ............ eq. no. (iii)

The simultaneous equations have infinitely many solutions.

a1/a2 = b1/b2 = c1/c2
∴ ¼ = 1/k = ¼
∴ ¼ = 1/k


k = 4

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