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Understanding and Graphing Systems of Inequalities

This educational resource focuses on graphing linear inequalities and understanding systems of inequalities. It outlines essential steps: graphing related linear equations, using solid or dashed lines for inequalities, and shading the correct solution regions. The content includes practical examples for students to apply, emphasizing the importance of adjusting symbols when multiplying or dividing by negative numbers. Perfect for learners looking to master graphing techniques in the coordinate plane and apply inequalities to real-world scenarios.

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Understanding and Graphing Systems of Inequalities

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  1. 7.5 Systems of Inequalities Objectives • The learner will graph linear inequalities. NCSCOS • 4.03

  2. 7.5 Systems of Inequalities Graphing a Linear Inequality in the Coordinate Plane 1. Graph the related linear equation. • Use a solid line • for  or . • Use a dashed line • for < or >.

  3. 7.5 Systems of Inequalities • ymx + b • y mx + b Shade the above the line: Shade below the line: • ymx + b • y mx + b

  4. 7.5 Systems of Inequalities • x c • x < c Shade left of the line: Shade right of the line: • x c • x> c

  5. 7.5 Systems of Inequalities Summary for Graphing Linear Inequalities 1. Solve for y = mx + b 2.Remember: change the symbol if you multiply or divide by a negative number. 3. Draw the boundary line (solid or dashed). 4. Shade the solution region (above or below,left or right).

  6. 7.5 System of Inequalities Graph the inequality: 1 2 y  x – 2

  7. 7.5 System of Inequalities Graph the inequality: y  3x – 2

  8. 7.5 System of Inequalities Graph the inequality: 2x – y  -3 –y  –2x – 3 y  2x + 3

  9. 7.5 System of Inequalities Graph the inequality: 73 23 y  x +

  10. 7.5 System of Inequalities Graph the inequality: 2x + 3y  6 3y  –2x + 6 23 y  - x + 2

  11. y – x – 1 y x + 3 7.5 Systems of Inequalities Graph the inequalities: 12

  12. y > –x + 3 y x + 2 7.5 Systems of Inequalities Graph the inequalities:

  13. y x – 3 y < – 2x + 1 7.5 Systems of Inequalities Graph the inequalities: 34

  14. 3x – y –2 x – y –1 7.5 Systems of Inequalities Graph the inequities: y  3x + 2 y  x + 1

  15. y –4x + 7 y –2x – 6 7.5 Systems of Inequalities Graph the inequalities: Another way to graph inequalities: shade below shade above

  16. y <3x + 1 y < -x + 5 Graph the inequalies: shade below shade below

  17. y >2x + 2 y > -x – 1 7.5 Systems of Inequalities Graph the inequalities: shade above shade above

  18. y < -2x y > – x – 3 7.5 Systems of Inequalities Graph the inequalities: shade below 1 2 shade above

  19. y < – x + 1 y > 2x – 7 7.5 Systems of Inequalities Graph the inequalities: 1 5 shade below shade above

  20. 3x + y < 4 x – 2y < 6 7.5 Systems of Inequalities Graph the inequalities: y < -3x + 4 1 2 y > x – 3 shade below shade above

  21. -2x + y < 3 3x – y > -5 7.5 Systems of Inequalities Graph the inequalities: y < 2x + 3 y < 3x + 5 shade below shade below

  22. 7.5 Systems of Inequalities During the summer, Kara wants to earn at least $126 per week by working part-time. She can make $6 an hour doing yard work and $7 an hour working at the library. She can work no more than 30 hours each week. Write a system of inequalities to represent Kara’s situation, and then graph the results.

  23. 7.5 Systems of Inequalities Graph the inequalities: The intersection of the brown area will meet both of Kara’s needs. 40 y  –x + 30 30 76 y  - x + 21 20 shade below 10 shade above 2 4 6 8 10 12 14

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