1. Copyright © 2008 Pearson Education Canada4-1 Chapter 4 Linear Systems Contemporary Business Mathematics with Canadian Applications Eighth Edition S. A. Hummelbrunner/K. Suzanne Coombs PowerPoint: D. Johnston

2. Copyright © 2008 Pearson Education Canada4-2 Objectives After completing chapter four the student will be able to: Use the method of elimination to solve a linear system of two simultaneous equations in two variables. Graph linear equations. Graph linear systems of two equations with two variables. Solve problems using linear systems.

3. Copyright © 2008 Pearson Education Canada4-3 Algebraic Elimination Method

4. Copyright © 2008 Pearson Education Canada4-4 Algebraic Elimination Method (continued)

5. Copyright © 2008 Pearson Education Canada4-5 Unequal Coefficients

6. Copyright © 2008 Pearson Education Canada4-6 Graphing Linear Equations

7. Copyright © 2008 Pearson Education Canada4-7 Locating a Point

8. Copyright © 2008 Pearson Education Canada4-8 Constructing a Table for x + y = 4

9. Copyright © 2008 Pearson Education Canada4-9 Graphing an Equation x + y = 4

10. Copyright © 2008 Pearson Education Canada4-10 Special Cases Lines Parallel to X-axis Note the graphs for y = 3 and y = -3.

11. Copyright © 2008 Pearson Education Canada4-11 Special Cases Lines Parallel to Y-axis Note the graphs of x =3 and x = -3.

12. Copyright © 2008 Pearson Education Canada4-12 Slope-y-intercept Form of a Linear Equation

13. Copyright © 2008 Pearson Education Canada4-13 Writing an Equation in Slope-y-intercept Form

14. Copyright © 2008 Pearson Education Canada4-14 Special Cases for the Slope

15. Copyright © 2008 Pearson Education Canada4-15 Different Cases for the Slope

16. Copyright © 2008 Pearson Education Canada4-16 Graph a System of Linear Equations x = y x-2y +2000 = 0

17. Copyright © 2008 Pearson Education Canada4-17 Problem Solving

18. Copyright © 2008 Pearson Education Canada4-18 Problem Solving (continued)

19. Copyright © 2008 Pearson Education Canada4-19 Summary Linear systems of two simultaneous equations in two variables are useful for modelling business applications. Such systems can be solved by graphing the two linear equations and finding the point of intersection. Such systems can be solved algebraically by using the method of elimination.