• # question_answer The value of k, for which the system of equations $kx-3y+6=0,\text{ }4x-6y+15=0$represent parallel lines, is ____.      A)  1                                 B)  2                     C)  3                     D)         4

It is given that, $kx-3y+6=0$and $4x-6y+15=0$are two parallel lines,                       i.e., The given lines has no solution or         $\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}\ne \frac{{{c}_{1}}}{{{c}_{2}}}$ $\Rightarrow$  $\frac{k}{4}=\frac{-3}{-6}\ne \frac{6}{15}$  $\Rightarrow$ $\frac{k}{4}=\frac{3}{6}$ $\Rightarrow$ $k=2$