Key Idea: One Solution (Linear System)

A linear system has one solution when the two equations represent lines with different slopes, meaning they intersect at exactly one point.

General Rule:

• Slopes are different.

• One point of intersection exists.

• This single point satisfies both equations simultaneously.

Why this matters for the SAT:

Identifying when a system has one solution is key to solving systems efficiently, whether by substitution, elimination, or graphing. Different slopes guarantee a unique solution.