1. 6/21/2016Math 120 - KM1 Chapter 4: Systems of Equations 4.1 Systems of Equations in Two Variables 4.2 Solving by Substitution 4.3 Solving by Elimination 4.4 Solving Applied Problems: Two Equations 4.5 Systems of Equations in Three Variables 4.6 Solving Applied Problems: Three Equations 4.7 Systems of Inequalities in Two Variables

2. 6/21/2016Math 120 - KM2 4.1 Systems of Equations in Two Variables 4.1

3. 6/21/2016Math 120 - KM3 Types of Systems A consistent system has at least one solution one point or the whole line The lines intersect! 4.1

4. 6/21/2016Math 120 - KM4 Types of Systems An inconsistent system has no solution. The lines do NOT intersect! 4.1

5. 6/21/2016Math 120 - KM5 Systems of Equations In order to solve a system of equations by graphing: Graph each of the lines using the best method. Plot x and y-intercepts Plot other Points Use Point Slope The point(s) where the lines intersect are in the solution set. 4.1

6. 6/21/2016Math 120 - KM6 Where will they meet? 4.1

7. 6/21/2016Math 120 - KM7 How about this pair? 4.1

8. 6/21/2016Math 120 - KM8 What if? 4.1

9. 6/21/2016Math 120 - KM9 How about these lines? 4.1

10. 6/21/2016Math 120 - KM10 4.2 Solving by Substitution 4.2

11. 6/21/2016Math 120 - KM11 Systems of Equations In order to solve a system of equations by substitution: Solve one equation for x or for y (pick the easiest one). Substitute for that letter in the OTHER equation. Solve this equation for the variable. Substitute the answer back into the original equation. 4.2

12. 6/21/2016Math 120 - KM12 No Graph? 4.2

13. 6/21/2016Math 120 - KM13 Let’s Check the Answer 4.2

14. 6/21/2016Math 120 - KM14 Another Substitution 4 U ! 4.2

15. 6/21/2016Math 120 - KM15 Be Sure to Check the Answer! 4.2

16. 6/21/2016Math 120 - KM16 Would I Try to Fool You? NO WAY! 4.2

17. 6/21/2016Math 120 - KM17 Guess what? 4.2

18. 6/21/2016Math 120 - KM18 Check To Be Sure! 4.2

19. 6/21/2016Math 120 - KM19 OK…last one for now! 4.2

20. 6/21/2016Math 120 - KM20 Problem continued! 4.2

21. 6/21/2016Math 120 - KM21 4.3 Solving by Elimination 4.3

22. 6/21/2016Math 120 - KM22 Look for the Opposites 4.3

23. 6/21/2016Math 120 - KM23 Could it happen again? 4.3

24. 6/21/2016Math 120 - KM24 The LCM is the KEY! 4.3

25. 6/21/2016Math 120 - KM25 I think you get it! 4.3

26. 6/21/2016Math 120 - KM26 Silent Movie! 4.3

27. 6/21/2016Math 120 - KM27 4.4 Solving Applied Problems: Two Equations 4.4

28. 6/21/2016Math 120 - KM28 Pairs of Angles! 4.4

29. 6/21/2016Math 120 - KM29 C Complements 4.4

30. 6/21/2016Math 120 - KM30 S Supplements 4.4

31. 6/21/2016Math 120 - KM31 Angles not Angels! Two angles are complementary. The larger angle is 9 o more than eight times the measure of the smaller angle. Find the measures of the two angles. 9 o and 81 o 4.4

32. 6/21/2016Math 120 - KM32 Where We Left Off Last Class

33. 6/21/2016Math 120 - KM33 Tail Wind Head Wind With the WindAgainst the Wind Speeds you up Slows you down With / Against 4.4

34. 6/21/2016Math 120 - KM34 Let’s go flying! Flying with the wind, a small plane flew 300 miles in 2 hours. Against the wind the plane could only fly 270 miles in the same amount of time. Find the rate of the plane in calm air and the rate of the wind. The plane in calm air can go 142.5 mph and the wind is 7.5 mph 4.4

35. 6/21/2016Math 120 - KM35 How about boating? A motorboat traveling with the current went 72 km in 3 hours. Against the current, the boat could go only 48 km in the same amount of time. Find the rate of the boat in calm water and the rate of the current. The boat can go 20 kph in calm water. The current is 4 kph 4.4

36. 6/21/2016Math 120 - KM36 Mrs. Peterson’s horse Red Rider needs 25 pounds of food, with an average of 9% protein, a day. Alfalfa contains 8% protein and rolled oats contain 12% protein. How many pounds a day of alfalfa and rolled oats should she feed Red? Red’s Diet 4.4

37. 6/21/2016Math 120 - KM37 QUANTITY: 25 pounds total Pounds and Protein Quantity and Quality QUALITY: 9% Protein A = pounds of Alfalfa R = pounds of Rolled Oats A + R = 25 0.08A + 0.12R = (0.09)25 4.4

38. 6/21/2016Math 120 - KM38 Red’s Diet System 100∙ -8∙ 4.4

39. 6/21/2016Math 120 - KM39 And Red should get... A + R = 25 A = 18.75 18.75 pounds of Alfalfa and 6.25 pounds of Rolled Oats. 4.4

40. 6/21/2016Math 120 - KM40 Mixed Up Money? A piggy bank contains twenty-four nickels and quarters. The coins have a total value of $3.20. Determine the number of nickels and the number of quarters in the bank ? 4.4

41. 6/21/2016Math 120 - KM41 QUANTITY: 24 coins total # Coins and Value Quantity and Quality QUALITY: total value $3.20 N = # of Nickels Q = # of Quarters N + Q = 24 0.05N + 0.25Q = 3.20 4.4

42. 6/21/2016Math 120 - KM42 Piggy’s Coin System 100∙ -5∙ 4.4

43. 6/21/2016Math 120 - KM43 How many of each? N = 14 Pig E. Bank had 14 Nickels and 10 Quarters. 70 ¢ + $2.50 = $3.20 4.4

44. 6/21/2016Math 120 - KM44 Back in the Lab! The chemistry stock room contains barrels of 10% alcohol and 50% alcohol. How much of each must be mixed to get a total of 100 liters of a 40% solution? Weak + Strong = Medium 4.4

45. 6/21/2016Math 120 - KM45 QUANTITY: 100 Liters total Liters and Strength Quantity and Quality QUALITY: final strength 40% W = # of liters of 10% CH 3 CH 2 OH W + S = 100 0.10W + 0.50S = (0.40)100 S = # of liters of 50% CH 3 CH 2 OH 4.4

46. 6/21/2016Math 120 - KM46 Our Chemistry System 10∙ -1∙ 4.4

47. 6/21/2016Math 120 - KM47 We’re Almost Done! W + S = 100 W = 25 25 liters of 10% alcohol and 75 liters of 50% alcohol will make 100 liters of 40% alcohol. 4.4

48. 6/21/2016Math 120 - KM48 Need Stamps? A postal clerk sold some 22 cent and some 28 cent stamps. Altogether he sold 120 stamps for a total cost of $28.20. How many of each type stamp were sold? LET C = # of 22 cent stamps E = # 28 cent stamps 4.4

49. 6/21/2016Math 120 - KM49 Cheap + Expensive = Medium -22∙ 100∙ 90 @ 22 cent stamps 30 @ 28 cent stamps 4.4

50. 6/21/2016Math 120 - KM50 4.5 Systems of Equations in Three Variables 4.5

51. 6/21/2016Math 120 - KM51 Too Spacey? { (3, -1, 2) } 4.5

52. 6/21/2016Math 120 - KM52 Keep Track! { (-1,2,1) } 4.5

53. 6/21/2016Math 120 - KM53 { (4, 1, 5) } Something missing? 4.5

54. 6/21/2016Math 120 - KM54 3.6 Solving Applied Problems Three Equations (x, y, z) 4.6

55. 6/21/2016Math 120 - KM55 A Puzzle 4 U The sum of three numbers is 20. The difference between the largest and the smallest is 29. The sum of the two smaller numbers is -2. What are the numbers? -7, 5, and 22 4.6

56. 6/21/2016Math 120 - KM56 What’s for Dinner? A patient is limited to 800 calories for dinner with 55g of protein and 220 mg of vitamin C using servings of the following food items: Meat 2, Potato 1, Veggie 2 1 servingcaloriesproteinVit C meat300200 potato100520 vegetable505100 4.6

57. 6/21/2016Math 120 - KM57 4.7 Systems of Inequalities in Two Variables 4.7

58. 6/21/2016Math 120 - KM58 Shady Problems? On this side all the x- coordinates are greater than 2 On this side all the x- coordinates are less than 2 4.7

59. 6/21/2016Math 120 - KM59 Another One? 4.7

60. 6/21/2016Math 120 - KM60 Two at a time! 4.7

61. 6/21/2016Math 120 - KM61 You can do these! 4.7

62. 6/21/2016Math 120 - KM62 Through the Origin? 4.7

63. 6/21/2016Math 120 - KM63 WOW!!! 4.7

64. 6/21/2016Math 120 - KM64 That’s All For Now!

65. 6/21/2016Math 120 - KM65 Word Problem Handout Let’s Go Flying: Flying with the wind, a small plane flew 300 miles in 2 hours. Against the wind the plane could only fly 270 miles in the same amount of time. Find the rate of the plane in calm air and the rate of the wind. How about Boating? : A motorboat traveling with the current went 72 km in 3 hours. Against the current, the boat could go only 48 km in the same amount of time. Find the rate of the boat in calm water and the rate of the current. Red’s Diet” Mrs. Peterson’s horse Red Rider needs 25 pounds of food, with an average of 9% protein, a day. Alfalfa contains 8% protein and rolled oats contain 12% protein. How many pounds a day of alfalfa and rolled oats should she feed Red? Mixed Up Money: A piggy bank contains twenty-four nickels and quarters. The coins have a total value of $3.20. Determine the number of nickels and the number of quarters in the bank ? Back in the Lab: The chemistry stock room contains barrels of 10% alcohol and 50% alcohol. How much of each must be mixed to get a total of 100 liters of a 40% solution? Need Stamps: A postal clerk sold some 22 cent and some 28 cent stamps. Altogether he sold 120 stamps for a total cost of $28.20. How many of each type stamp were sold?