Straight Lines And Pair Of Straight Lines

parallel lines if $\frac{a_i}{a_j} \neq \frac{b_i}{b_j} \neq \frac{c_i}{c_j}(i \neq j)$

coincident lines if $\frac{a_i}{a_j}=\frac{b_i}{b_j}(i \neq j)$

concurrent lines but not coincident if $\frac{a_i}{a_j}=\frac{b_i}{b_j}=\frac{c_i}{c_j}(i \neq j)$

concurrent lines if $\frac{a_i}{a_j} \neq \frac{b_i}{b_j} \neq \frac{c_i}{c_j}(i \neq j)$