Chapter 3 Linear Systems

Chapter 3 Linear Systems af Troy Cole

1. Chapter 3.2

2. Solving systems Algebraically

3. Equivalent systems: systems that have the same solution.

4. Chapter 3.3

5. Systems of Inequalities

6. Ex. x - 2y < 6 y< -3/2x + 5

7. Chapter 3.4

8. Linear Programming

9. Linear Programming: identifies the minimum and maximum.

10. Objective Function: is how the minimum is modeled.

11. Constraints: are the limits on the variables.

12. Feasible Region: is the area on a graph that satisfies all the constraints.

13. Chapter 3.5

14. Graphs in Three Dimension

15. Coordinate Space: is adding a third axis, "z".

16. Ordered Triplets: (X,Y,Z)

17. Trace: when the graph of a pkane intersects one of the coordinate planes in a line.

18. Chapter 3.6

19. Systems with Three Variables

20. Paired for elimination x - 3y + 3z = -4 2x + 3y - z = 15 --------------------- 3x + 2z = 11

21. Solve for "x" 3x + 2z = 11 6x - 2z = 34 ----------------- 9x =45 x=5

22. Graphing Systems of Equations

23. Chapter 3.1

24. System of equations: a set of two or more equations that use the same variables.

25. Linear System: a line that contains two identicle variables.

26. Independent system: has a unique solution.

27. Dependnt system: does not have a unique solution.

28. Ex. y= x + 3 y= -2x + 3

29. Inconsistant system: a system that does not have a solution.

30. Subsitution Ex. 4x + 3y = 4 2x - y = 7

31. Solve for "y" 2x - y = 7 y= 22 -7

32. Subsitute the "y" 4x + 3y =4 4x + 3(2x - 7) =4 4x + 6x - 21 =4 4x + 6x =25 x=2.5.

33. Solve for "y" again y= 2x - 7 y= 2(2.5) - 7 y= -2

34. Final Answer (2.5, -2)

35. Three Systems x - 3y + 3z = -4 2x + 3y - z = 15 4x - 3y - z = 19

36. and....

37. Paired for elimination 2x + 3y - z = 15 4x - 3y - z = 19 ---------------------- 6x - 2z = 34

38. Solve for "z" 3x + 2z =11 3(5) + 2z = 11 ------------------- 2z = -4 z=-2

39. Solve by subsitution x - 3y + 3z = -4 5 - 3y + 3(-2) = -4 5 - 3y - 6 = -4 -3y = -3 y=1

40. Final answer (5,1,-2)