Question

If $am=bl,$ then find whether the pair of linear equations $ax+by=c$ and $lx+my=n$ has no solution,unique solution or infinitely many solutions.

Answer 1

Using the pair of linear equation formula

$am=bl$

$\frac{a}{l}=\frac{b}{m}$

$ax+by-c=0$

$lx+my-n=0$

$\frac{a_1}{a_2}=\frac{a}{l}$

$\frac{b_1}{b_2}=\frac{b}{m}$

$\frac{c_1}{c_2}=\frac{-c}{-n}$

$\frac{a}{l}-\frac{b}{m}\ne \frac{-c}{-n}$

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

$\therefore$ The pair of equation has no solutions