Defining Linear Inequalities in Two Variables Q2.ppt
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This document defines and provides examples of linear inequalities in two variables. It begins by introducing linear inequalities and their standard forms. An example inequality models the work hours of a student Manuel to earn at least $825 per week. Ordered pairs are then tested as solutions by substituting their values into the inequality. Additional examples demonstrate determining if ordered pairs satisfy other inequalities. The document concludes with an activity for the reader to practice identifying solution ordered pairs.
Defining Linear Inequalities in Two Variables Q2.ppt
- 1. Defining a Linear Inequality in Two Variables
- 2. What you’ll learn: 1. Review the definition of inequality. 2. Translate real-life situation to linear inequality Think critically and divergently!
- 3. A Working Student’s Schedule Manuel has two part time jobs, one paying Php 30 per hour and another paying Php 35 per hour. He must earn at least Php 825 per week to pay his expenses while attending college night classes. Write an inequality that shows the various ways he can schedule his time to achieve his goal.
- 4. Let x = the no. of hours Manuel works on the first job y = the no. of hours Manuel works on the second job The hourly rate on the first job no. of hours worked on the first job The hourly rate on the second job no. of hours worked on the second job Php 825 is at least 30 35 x y 825 825 35 30 y x
- 5. 825 35 30 y x The inequality obtained is an example of a linear inequa In two variables. A linear inequality in two variables can be written in one of four forms: C By Ax C By Ax C By Ax C By Ax where A, B and C represent real numbers and A and B Are not both zero.
- 6. Symbols used in inequality. Greater than Less than Greater than or equal to ; at least Less than or equal to ; at most
- 7. An ordered pair (x, y), is a solution of an inequality in two variables if a true statement results when variables in the inequality are replaced by the coordinates of the ordered pair. So, let us determine whether each ordered pair is a solution of the given inequality…
- 8. Example 1: Determine whether each ordered pair is a solution of 825 35 30 y x a. (6, 15) b. (10, 15) c. (12, 16)
- 9. SOLUTIONS: a. (6, 15) 825 35 30 y x 825 ) 15 ( 35 ) 6 ( 30 Substitute 6 for x and 15 for y . 825 525 180 825 705 FALSE Hence, (6, 15) is NOT a solution of the inequality.
- 10. SOLUTIONS: b. (10, 15) 825 35 30 y x 825 ) 15 ( 35 ) 10 ( 30 Substitute 10 for x and 15 for y . 825 525 300 825 825 TRUE Hence, (10, 15) is a solution of the inequality.
- 11. SOLUTIONS: c. (12, 16) 825 35 30 y x 825 ) 16 ( 35 ) 12 ( 30 Substitute 12 for x and 16 for y . 825 560 360 825 920 TRUE Hence, (12, 16) is a solution of the inequality.
- 12. Example 2: Determine whether each ordered pair is a solution of 3 2 5 y x a. (-1, 0) b. (1, 2) c. (2, 1/2)
- 13. SOLUTIONS: a. (-1, 0) Substitute -1 for x and 0 for y . TRUE Hence, (-1, 0) is a solution of the inequality. 3 2 5 y x 3 ) 0 ( 2 ) 1 ( 5 3 0 5 3 5
- 14. SOLUTIONS: b. (1, 2) Substitute 1 for x and 2 for y . TRUE Hence, (1, 2) is a solution of the inequality. 3 2 5 y x 3 ) 2 ( 2 ) 1 ( 5 3 4 5 3 1
- 15. SOLUTIONS: c. (2, 1/2) Substitute 2 for x and 1/2 for y . FALSE Hence, (2, 1/2) is NOT a solution of the inequality. 3 2 5 y x 3 ) 2 / 1 ( 2 ) 2 ( 5 3 1 10 3 9
- 16. ACTIVITY: 1. Determine whether each ordered pair is a solution o 10 3 4 y x a. (1, 2) b. (3, 1) c. (-1/4, -2)
- 17. ACTIVITY: 2. Determine whether each ordered pair is a solution o 6 5 3 y x a. (-1, -2) b. (1, 2) c. (-5, 0)
- 18. ANSWERS: 1. Determine whether each ordered pair is a solution o 10 3 4 y x a. (1, 2) b. (3, 1) c. (-1/4, -2) SOLUTION NOT SOLUTION SOLUTION
- 19. ANSWERS: 2. Determine whether each ordered pair is a solution o 6 5 3 y x a. (-1, -2) b. (1, 2) c. (-5, 0) NOT SOLUTION SOLUTION NOT SOLUTION
- 20. Thank you for watching