As shown in the diagram above, two planes intersect in a line. We can find the equation of the line by solving the equations of the planes simultaneously, with one extra complication – we have to introduce a parameter. If we take the parameter at being one of the coordinates, this usually simplifies the algebra.

Example: Find the equation of intersection of the planesand

We take the parameter asand putThe equations become

(1)

(2)

(1)-2*(2) gives

Substituteinto (2)