For what value of k does the system of equations
` " " x + 2y = 3, 5x + ky + 7 = 0`
have (i) a unique solution, (ii) no solution ?
Also, show that there is no value of k for which the given system equations has infinitely many solutions.

Answer

(i) `k ne 10 ` (ii) `k = 10`

Explanation

(i) ` (1)/(5) ne (2)/(k) rArr k ne 10 `
(ii)` (1)/(5) = (2)/(k) ne (-3)/(7) rArr k = 10 `
Clearly, ` (1)/(5) = (2)/(k) = (-3)/(7) ` is never true, as ` (1)/(5) = ( -3)/(7) ` is false.