For what value of k will the following pair of linear equations have no solution ?
`" " 2x + 3y - 4 = 0 and 2x + 6y - 7 = 0`

Explanation

For no solution, we have ` (a_1)/(a_2) = (b_1)/(b_2) ne (c_1)/(c_2)`.
` therefore (2)/(6) = (3)/(k - 2 ) and (2)/(6) ne = (9)/(3k - 2) rArr ( 3)/(k - 2 ) = (1)/(3) and (9)/(3k - 2) ne (1)/(3)`
` rArr k - 2 = 9 and 3k - 2 ne 27 rArr k = 11 and k ne (29)/(3)`.
Hence, ` k = 11 `