Given pair of linear equations is
`kx + 3y = k - 3 " " ...(i) `
and `" " 12x + ky = k " " ...(ii)`
On comparing with `ax + by + c = 0`, we get
`a_(1) = k, b_(1) = 3` and `c_(1) = -(k - 3) " " ` [from Eq. (i)]
`a_(2) = 12, b_(2) = k` and ` c_(2) = -k " " `[from Eq. (ii)]
For no solution of the pair of linear equations,
`(a_(1))/(a_(2)) = (b_(2))/(b_(2)) != (c_(1))/(c_(2))`
`rArr " " (k)/(12) = (3)/(k) != (-(k - 3))/(-k)`
Taking first two parts, we get
`rArr " " (k)/(12) = (3)/(k)`
`rArr " " k^(2) = 36`
`rArr " " k +- 6`
Taking last two parts, we get
`(3)/(k) != (k - 3)/(k)`
`rArr " " 3k != k (k - 3)`
`rArr " " 3k - k (k - 3) != 0`
`rArr " "k( 3-k + 3) != 0`
`rArr " " k(6 - k) != 0`
`rArr " " k !=0` and `!= 6`
Hence, required value of k for which the given pair of linear equations has no solution is - 6.
