4y = kx – 10; 3x = 2y + 5

(ii) 4y = kx – 10; 3x = 2y + 5

Sol. 4y = kx – 10
∴  – kx + 4y = – 10
Comparing with a1x + b1y = c1 we get, a1 = – k, b1 = 4, c1 = – 10

3x = 2y + 5
∴  3x – 2y = 5
Comparing with a2x + b2y = c2 we get, a2 = 3, b2 = – 2, c2 = 5

a1/a2 = -k/3 = -k/3  ............ eq. no. (i)
b1/b2 = 4/-2 = -2 ............ eq. no. (ii)
c1/c2 = -10/5 = -2  ............ eq. no. (iii)

The simultaneous equations have infinitely many solutions.

a1/a2 = b1/b2 = c1/c2
∴ -k/3 = -2 = -2
∴ -k/3 = -2
- k  = - 6


k = 6

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