The value of c for which the

(d) Condition for infinitely many solutions

$\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$ $\ldots$ (i)

The given lines are $c x-y=2$ and $6 x-2 y=3$

Here, $a_{1}=c_{1} b_{1}=-1, c_{1}=-2$

and $a_{2}=6, b_{2}=-2, c_{2}=-3$

From Eq. (i), $\frac{c}{6}=\frac{-1}{-2}=\frac{-2}{-3}$

Here, $\frac{c}{6}=\frac{1}{2}$ and $\frac{c}{6}=\frac{2}{3}$

$\Rightarrow$ $c=3 \quad$ and $\quad c=4$

Since, c has different values.

Hence, for no value of c the pair of equations will have infinitely many solutions.