Chapter 3 Linear Systems
by 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)
