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Solving Systems of Inequalities by Graphing: Dashed vs Solid Lines and Shading Regions

This guide explains how to solve systems of inequalities through graphing. Learn how to determine if a line is dashed or solid based on the inequality symbols (<, >, ≤, ≥) and how to find a test point outside the boundary, typically (0, 0), for analysis. The process includes converting inequalities to slope-intercept form and graphing related equations while carefully shading the correct regions based on test point results. Additionally, review examples demonstrating overlapping and non-overlapping solution regions, ensuring clear understanding for homework application.

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Solving Systems of Inequalities by Graphing: Dashed vs Solid Lines and Shading Regions

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  1. 3-3 Solving Systems of Inequalities by Graphing

  2. Determine if line is dashed/solid (< or > ----->, ≤ or ≥ →) Plug in any pt not on boundary (0, 0) is simplest if available Find related equation ex) y < 5x + 6, y = 5x + 6 Put inequality in slope-int form y = mx + b Graph the related equation DO NOT SHADE THIS REGION!! SHADE OTHER ONE! Shade the region where the test point resides Review: Graphing Inequalities FALSE TRUE

  3. Identify the Solution Graph 2nd inequality (Solution: one shaded region in another color) Graph the 1st inequality (Solution: one shaded region) NO SOLUTION! ALL POINTS IN THE OVERLAPPED SHADING ARE SOLUTIONS Solving a System of 2 Inequalities SHADINGS OVERLAP NO OVERLAP

  4. Ex 1

  5. Ex 1

  6. Ex 2

  7. Ex 3

  8. Ex 4

  9. Homework • Text p. 126 (12-26 all)

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