
Then (x1, y1) lies on both (i) and (ii).
Solving for x1 and y1 by the method of cross multiplication, we obtain

Thus, the point of intersection is obtained by solving the two given equations.
Remark:
(i) and (ii) are not parallel if they intersect
their slopes are not equal.
(ii) If a1b2 - a2b1 = 0, then the coordinates of the points of intersection is not defined. In this case the lines are parallel.
