Linear Inequalities and Graphing

These flashcards cover key terms and definitions related to systems of linear inequalities, their graphing processes, and related concepts.

Systems of Linear Inequalities

Inequalities involving two or more variables where the solutions are represented by regions in the graph.

Compound Inequalities

An inequality that consists of two inequalities joined by 'and' or 'or'.

Graphing Linear Inequalities Steps

1. Graph the boundary line of each inequality. 2. Determine if the boundary line is solid or dashed.

Solid Line

Indicates that points on the line are included in the solution (≥ or ≤).

Dashed Line

Indicates that points on the line are excluded ( > or <).

Boundary Line

The line defined by an equation that separates the solution regions in the graph.

Testing Ordered Pairs

Substituting a point into an inequality to determine if it satisfies the inequality.

Combined Solution Set

The area where the shaded regions from multiple inequalities overlap.

Compound Inequalities Graphing

Treat as two separate inequalities when graphing, indicating overlapping solution areas on the graph.

Summary of Graphing Process

1. Graph each inequality. 2. Determine boundary type. 3. Shade appropriate regions. 4. Identify intersection of shaded areas.