Hi

You have several ways to find a parametric equation of the line of intersection

You can find 2 points on the line

Take for instance x=3, solve the system

Then take x=-1, solve the system

These 2 points define one direction vector of the line

Since you already have 1 point of the line, you can get a parametric equation

Second method, solve the system

using z (for instance) as parameter

You will find x, y (and z) function of z (parameter)