If a1x + b1 y + c1 = 0
a2x + b2y + c2 = 0
is a pair of linear equations in two variables x and y such that :
(i) \(\frac{a_1}{a_2}\) \(\ne\) \(\frac{b_1}{b_2}\),then the pair of linear equations is consistent with a unique solution, i.e., they intersect at a point.
(ii) \(\frac{a_1}{a_2}\) = \(\frac{b_1}{b_2}\) \(\ne\) \(\frac{c_1}{c_2}\),then the pair of linear equations inconsistent with no solution, i.e., they represent a pair of parallel lines.
(iii) \(\frac{a_1}{a_2}\) = \(\frac{b_1}{b_2}\) = \(\frac{c_1}{c_2}\), then the pair of linear equations are consistent with infinitely many solutions, i.e., they represent coincident lines.
