A plane in three dimensional space can be written as ax + by + cz = d. We can find the possible intersections of planes in this form by writing them as systems of linear equations and using reduction to solve them. If d = 0 in each equation, then we have a homogeneous system with either a unique solution or infinitely many solutions.Determine whether the intersection of the planes: has a unique solution or infinitely many solutions; then solve the system.

Question

What will be an ideal response?

Answer 1

infinitely many solutions; x- z = 0, y + 1z = 0; in parametric form: x = r, , z = r, where r is any real number.