SAT Math Lesson 4: Systems of Linear Inequalities

This 45-minute lesson is part of Media4Math’s 35-lesson SAT Math prep series. It focuses on solving and graphing systems of linear inequalities—a topic within the Heart of Algebra domain, which makes up about 33% of the SAT Math section. Students will learn how to graph inequalities on the coordinate plane, determine boundary line types, apply test points, and find the region where multiple inequalities intersect.

Through five fully worked-out instructional examples, students build a strong conceptual foundation in graphing systems, including how to interpret inequality symbols, use slope-intercept form, and understand graphical shading. The lesson also includes a real-world application problem to show how systems of inequalities are used in practical contexts such as budgeting and resource constraints. A review section reinforces key concepts with three additional examples, followed by a 10-question multiple-choice quiz and detailed answer key to assess mastery.

Clear visuals, step-by-step explanations, and self-study tips throughout the lesson make it ideal for classroom instruction, tutoring, or independent SAT preparation. This lesson aligns with Common Core standards and mirrors the types of reasoning required for success on the SAT Math section.

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