(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
