Point of intersection of two lines

Then (x₁, y₁) lies on both (i) and (ii).

Solving for x₁ and y₁ by the method of cross multiplication, we obtain

Hence the point of intersection is

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.

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Subjects
English
Math
Geometry