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Section 8.5

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

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Section 8.5

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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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