When two curves intersect they have the same x and y values This means that given the equations of the curves, we can solve them like simultaneous equations to find the points of intersection.

Example: Find the points of intersection of the curve(1) and(2).

The curve and the line are illustrated below.

We can put (1)=(2) to getand multiply throughout byto clear all the fractions.

Subtract 3 from both sides, factorise and solve.

soor

Ifthen from (2)and ifthen from (2)