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Understanding Systems of Inequalities: Graphing Methods and Solutions

This section provides an overview of solving systems of inequalities through graphing. A system of inequalities consists of two or more inequalities involving two or more variables, which are combined to find a solution set of ordered pairs that satisfy both inequalities. The process involves writing inequalities in slope-intercept form and graphing them, paying attention to whether the boundary lines are solid or dashed based on the inequality symbols. The correct region representing the solution must be shaded, and the origin can be used as a test point for accuracy.

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Understanding Systems of Inequalities: Graphing Methods and Solutions

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  1. Section 8.5 What we are Learning: To solve systems of inequalities by graphing

  2. What is a System of Inequalities? • Two or more inequalities with two or more variables in them • They are used together to solve a problem • The solution to the system is the set of all ordered pairs which satisfies (answers) both inequalities

  3. How to Solve Systems of Inequality by Graphing: • We follow the same steps as solving Systems of Equations by graphing • Write each inequality in slope-intercept form • Slope-intercept form: y > mx + b • Carefully graph each inequality • The graph of each inequality is called a half-plane

  4. Remember: • If an inequality is ≤ or ≥ • The boundary/line representing the graph will be solid • ≤ reads less than or equal to • ≥ reads greater than or equal to • If an inequality is < or > • The boundary/line representing the graph will be dashed • < reads less than • > reads greater than

  5. Remember: • When graphing inequalities on a coordinate plane we must shade the region that makes the inequality true. • The origin (0, 0) is a good point to use. • If the origin make the inequality true, shade the region that contains the origin • If the origin makes the inequality FALSE, shade the region that DOES NOT contain the origin

  6. Example: • x < 1 x > -4 Solution: the shaded region between -4 and 1

  7. Example: • y ≥ 2x + 1 y ≤ -x + 1 Solution: Where the hatch marks meet

  8. Let’s Work This Together: • y – x < 1 y – x > 3

  9. Let’s Work This Together: • 2x + y ≤ 4 3x – y ≥ 6

  10. Homework: • Page 485 • 17 to 31 odd

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