Key Idea: No Solution (Linear System)

A linear system has no solution when the two equations represent parallel lines.

General Rule:

• Both lines have the same slope.

• Lines have different y-intercepts.

• The lines never intersect, so no point satisfies both equations.

Why this matters for the SAT:

Recognizing when a system has no solution prevents mistakes in solving and helps classify the system correctly (unique solution, no solution, or infinitely many solutions).