I use this investigation to have students discover the three distinct types of linear systems: dependent, inconsistent & independent/consistent.
Students will 1st solve and graph a system with 1 unique point of intersection (solution). Then they will solve an inconsistent system. Then they will solve a dependent system. They will be asked why there is not 1 solution for both dependent and inconsistent.
Finally, there will be extra practice followed by a student made glossary to define and identify the differences between the three types of linear systems.