Algebra 47 - Describing Infinte Solution Sets Parametrically

The video tutorial explains how systems of three linear equations in three variables can have infinitely many solutions when the intersection of the planes forms a line. It demonstrates the elimination method to solve such systems and shows how to create parametric equations to represent the solutions. The tutorial highlights the consistency of results regardless of the variable eliminated and discusses the variability in parametric equations that can describe the same solution set.

What happens when we choose different pairs of equations to eliminate a variable?

What is the role of the parameter T in parametric equations?

Discuss the importance of the ordered triple in the context of linear equations.

Why do we always end up with the equation 0 equals 0 when eliminating variables?