System of linear equation have no solution, $\therefore\,\,\,$ determinant of coefficient = 0 \left| {\matrix{ {k + 2} & {10} \cr k & {k + 3} \cr } } \right| = 0 $\Rightarrow$ $\,\,\,\,$ (k + 2) (k + 3) $-$ 10 K = 0 $\Rightarrow$ $\,\,\,\,$ k 2 $-$ 5k + 6 = 0 $\therefore\,\,\,\,$ k = 2, 3 When, k = 2 then equations become, 4x + 10y = 2 and 2x + 5y = 1 It has in finite number of solutions. When k = 3, equations becomes 5x + 10y = 3 3x + 6y = 2 Those equation has no solutions. $\therefore\,\,\,\,$ When k = 3, then system of equations have no solutions.