Question

write the condition for no solution and infinite solutions for two lines.

Answer 1

Two lines $ax+by+c=0$ and $mx+ny+p=0$ have no solution if they are parallel and not intersecting, and the condition is

$\frac{a}{m}=\frac{b}{n}\ne \frac{c}{p}$

They have infinite solution if the lines are concurrent and the condition is

$\frac{a}{m}=\frac{b}{n}=\frac{c}{p}$