Question

Find the value of $c$ for which the pair of equations $cx-y=2$ and $6x-2y=3$ will have infinitely many solutions.

Answer 1

We know that,

For two linear equations to heave infinitely many roots,

$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

Here,

$\frac{a_1}{a_2}=\frac{c}{6},\frac{b_1}{b_2}=\frac{-1}{-2}=\frac{1}{2},\frac{c_1}{c_2}=\frac{2}{3}$

Since, $\frac{1}{2}\ne \frac{2}{3}$

$\therefore$ For no value of $c$, the given system of equations have infinitely many solutions.