U4D1 Solving Linear Systems by Graphing and System Classification

Vocabulary flashcards defining classifications of linear systems, conditions for the number of solutions, and geometric line relationships from the U4D1 graphing lecture.

Consistent system

A system of linear equations that has one or more solutions.

Inconsistent system

A system of linear equations that has no solution ($0$ solutions).

Parallel lines

Lines that share the same slope but have different y-intercepts, resulting in no points of intersection and $0$ solutions.

Coincident lines

Lines that share the same slope and the same y-intercept, lying directly on top of each other and producing infinitely many solutions ($\infty$ solutions).

System with one solution

A linear system where the lines have different slopes, intersecting at exactly one coordinate point $(x, y)$.

Solution to a linear system

The coordinate point $(x, y)$ representing the intersection of equations that makes every equation in the system true simultaneously.