1. Algebra A1Mr. Brennan Chapter 7 Systems of Linear Equations and Inequalities Review Hamilton-Wenham Regional High SchoolDepartment of Mathematics

2. Algebra A1Mr. Brennan Chapter 7 Review Systems of Linear Equations and Inequalities Hamilton-Wenham Regional High SchoolDepartment of Mathematics Learning Objectives: Chapter 7

3. Algebra A1Mr. Brennan Chapter 7 Review Systems of Linear Equations and Inequalities Hamilton-Wenham Regional High SchoolDepartment of Mathematics Learning Objectives: Chapter 7

4. The review for chapter 7 has three types of slides 1.Review material with goals and definitions 2.Examples with solutions (13) 3.Practice problems There are 30 practice problems for Chapter 7. Work out the problems as you encounter them. The answer to each question is displayed after each question. Systems of Linear Equations and Inequalities Chapter 7

5. Lesson 7.1 Solving Linear Systems by Graphing

6. Solution

10. Lesson 7.2 Solving Linear Systems by Substitution

11. Solution

15. Lesson 7.3 Solving Linear Systems by Linear Combinations

16. Solution

20. Lesson 7.4 Applications of Linear Systems: Exploring Data and Statistics

21. Solution

22. Sample answers are given here, there are multiple ways to solve each of these problems. a)Substitution method because the coefficient of x is one in the second equation, so x = 5 – 3y can be substituted into the first equation. Or 2x -3 = y can be used to substitute for y in the second equation. b) Use linear combinations – none of the variables have a coefficient of 1, or -1, though you could divide both sides of the first equation by 4 and get x + y = 4, then use substitution. c) Substitution method because the coefficient of x is one in the first equation

23. Solution

25. Lesson 7.5 Special Types of Linear Systems

26. Solution

28. Multiple methods can be used for any of these problems. 1.Using substitution you would end up showing -4 = -1 which is a false statement, so the system has no solution. Using a graphing method you would see that the lines are parallel, so the system has no solution. 2. Using substitution you would end up showing 5 = 7/3 which is a false statement, so the system has no solution. Using a graphing method you would see that the lines are parallel, so the system has no solution. 3. Using substitution you would end up showing 1 = -1 which is a false statement, so the system has no solution. Using a graphing method you would see that the lines are parallel, so the system has no solution.

29. Solution

30. Multiple methods can be used for any of these problems. 4. Using substitution you would end up showing 0 = 0 which is a true statement, so the system has infinitely many solutions. Using a graphing method you would see that the lines coincide, so the system has infinitely many solutions. 5. Using substitution you would end up showing 0 = 0 which is a true statement, so the system has infinitely many solutions. Using a graphing method you would see that the lines coincide, so the system has infinitely many solutions. 6. Using substitution you would end up showing 0 = 0 which is a true statement, so the system has infinitely many solutions. Using a graphing method you would see that the lines coincide, so the system has infinitely many solutions.

31. Solution

33. Lesson 7.6 Solving Systems of Linear Inequalities

34. Solution When graphing a system of linear inequalities, find each corner point (or vertex). The graph of the system for Example 1 has four corner points: (0, 0), (2, 2), (3, 2), and (3, -3).

35. Solution

37. The graph of the system of inequalities is shown. Any point in the shaded region is a solution of the system. Because you cannot buy a fraction of a disc or video, only ordered pairs of integers in the shaded region will answer the problem.

38. Solution