Name Class Period. Secondary 1 Honors Unit 6 ~ Systems of Equations

Transcription

1 Name Class Period Secondar 1 Honors Unit 6 ~ Sstems of Equations 1

2 Schedule for Unit 6 A-Da B-Da What we re doing Assignment What is due? Jan. 11 Jan : Graph Inequalities & Write Equations 6-1 Jan. 13 Jan : Graphing Sstems of Equations & Solving b Substitution WS Jan. 18 Jan : Solving b Elimination 6-3 WS 6-2 Jan. 20 Jan. 23 Quiz 6-2,3 6-4: Sstems of Inequalities Jan. 24 Jan. 2 Quiz : Sstems on the Graphing Calculator Jan. 26 Jan. 27 Quiz on : Sstems in Contet WS WS 6- WS 6-4 WS 6-6 WS 6- Jan. 30 Jan. 31 Review Review WS WS 6-6 Feb. 1 Feb. 2 Unit 6 Test Review WS 2

3 NOTES 6-1: Graphing Inequalities & Writing Equations Check whether the given ordered pair is a solution of E 1: (0, 1) E 2: (4, -1) Graphing a Linear Inequalit. Step 1: Step 2: Step 3: 3

4 Graph the following inequalities in a coordinate plane. E 3: < 2 E 4: E : < E 6:

5 E. 7: You and our famil have gone to a football game. Your mom sends ou to the concession stand to get food for everone. Nachos cost $3 and hamburgers cost $4. You spend $60 at the concession stand. a. Write an equation to represent this situation. b. List three different combinations of nachos and hamburgers ou could have purchased. E. 8: You open a savings account with $00. The bank tells ou that the will give ou an interest rate of 3.% annuall. Write an equation to represent this situation. E. 9: You start a hike with our friends miles awa from home. You and our group hike at a rate of 6 miles per hour. Write an equation to represent this situation.

6 HW 6-1: Graphing Inequalities & Writing Equations Instructions: You do NOT need to write out the entire stor problem, but ou DO need to define an variables that ou use, and be sure that ou do all parts. 1. When ou go to Little Caesar s to bu food for a famil part, ou find out the charge $ for each pizza and $2 for an order of breadsticks. You spend $0 on the food (before ta). a. Write an equation to represent this situation. b. List three different combinations of pizza and breadsticks ou could have purchased. 2. You purchase a car for $6000. The car depreciates in value b 8% each ear. Write an equation to represent this situation. 3. You purchase movie tickets for a group to attend the first showing of a movie. It costs $ for each adult ticket and $6.00 for each child ticket. You spent $60 on the tickets (before ta). a. Write an equation to represent this situation. b. List three different combinations of child and adult tickets ou could have purchased. 4. Dave is going on a backpacking trip. He has packed 62 pounds of food for the trip in his backpack. To ensure he has enough food for the trip he is eating 3 pounds of food each da. Write an equation to represent this situation.. The cit of Pthagoras started with a population of 34,000 people. The cit was growing at a rate of % each ear. Write an equation to represent this situation. 6. Becca is saving for a trip this summer. She starts a savings account with $20. She earns $ per week in allowance that she plans on putting into the account. Write an equation to represent this situation. Sketch a graph of each linear inequalit. Use the graph paper at the end of the packet, and attach it to our other work. 7. > >

7 Notes 6-2: Solving Sstems of Equations using Graphing & Substitution Sstems of Two Linear Equations: A Solution to a Sstem of Equations: Solve the sstem using a graph. E. 1: = 1 =

8 E. 2: = 4 = E. 3: = 2+ 2 = E. 4: 3+ = 2 =

9 Steps for Substitution Method: Step 1: Step 2: Step 3: Step 4: Step : Solve the sstem of equations using substitution. E. : = 3 8 = 4 E. 6: = 2 + = 6 9

10 Solve the sstem of equations using substitution. E. 7: 2+ 3= 2 + = 17 E. 8: 2+ 2= 3 4 = 1 E. 9: + = 22 = 2 HOMEWORK: WORKSHEET 6-2

11 Notes 6-3: Solving Sstems of Equations using Elimination Warm-up: Find the solution to the sstem of equations STOP HERE & WAIT! Zero Pairs: What does it take to add up to zero? E. 1: E. 3: 11

12 Common Denominators: What is the common denominator for the given fractions? E. 3: E. : E. 6: Elimination Method Step 1: Step 2: Step 3: Step 4: Step : 12

13 Solve the sstem of equations using elimination. E. 7: E. 8: E. 9: 13

14 Solve each sstem of equations b elimination. E. : E. 11: E. 12: E. 13: 14

15 HW 6-3: Solving Sstems of Equations Using Elimination For questions #1-12, solve using elimination. SHOW ALL WORK! Remember ou can check our solutions! For questions #13-21, solve using an method ou choose. Use graph paper at the end of the packet IF ou solve b graphing

16 Notes 6-4: Solving Sstems of Linear Inequalities Check whether the given ordered pair is a solution of E 1: (0, 1) E 2: (4, -1) E 3: (2, 1) Graphing a Sstem of Linear Inequalities. Step 1: Step 2: Step 3: 16

17 Graph the following inequalities in a coordinate plane. E 4: 3 1 < + 2 E : 2 3 > E 6: < 3 > 2 E 7: 2 > 4 2 < HOMEWORK: Worksheet

18 Notes 6-: Solving Sstems on a Graphing Calculator Eample 1: Use a graphing calculator to determine the best window to view the solution to the sstem of equations. Draw a quick sketch of the sstem in a standard window and in the best window. (Make sure ou draw our aes and label our min and ma for each ais.) a. b. = = f ( ) ( ) 1 = 4 g = Standard Window: Standard Window: Best Window: Best Window: Eample 2: Use the two sstems of equations above and our graphing calculator to solve the sstem. (Find the point(s) of intersection.) Write the solution below and label it on our graph above. Round the answers to the hundredths place, if necessar. a. b. 18

19 HOMEWORK: Worksheet 6. Notes 6-6: Sstems of Equations in Contet Provide the desired information about each situation given. You ma use our graphing calculator to find the graph and table of the information. Eample 1: You are having some friends over for a part this weekend at our house. Your parents have said ou have $60 that ou can spend on food, and ou ve decided to use that mone to bu pizzas and ice cream. Mace s has pizzas for $6.00 each and tubs of ice cream for $3.00 each. Smith s has pizzas for $4.00 each and tubs of ice cream for $4.00 each. a) Define our variables: b) Write our equations: c) Graph: Label aes, lines, intercepts and d) Table: Must go from -intercept intersection point. to -intercepts and include WHOLE # VALUES. Equation 1: Equation 2: Ordered Pairs Ordered Pairs e) What is the coordinate of intersection? 19

20 f) What does the intersection point mean in contet of the stor? g) If ou decide to spend all of our mone on pizza, which store should ou choose? Wh? How does this decision show up on the graph? h) If ou decide that ou need to bu 7 pizzas, which store will allow ou to bu more ice cream on our budget? How does this decision show up on the graph? 20

21 Eample 2: Addie and Ben are 1 ears old and are in 9 th grade right now. The decide to start saving up their mone to take a dream vacation one da. Addie puts $00.00 into a savings account and decides to deposit $4.00 into this special savings account ever ear. Ben puts $40.00 into a savings account and plans to just get more mone off of the interest he will earn. His account earns 7.% interest compounded annuall. a) Define our variables: b) Write our equations: c) Graph: Label aes, lines, intercepts and d) Table: Include values from 0 1. intersection point. : Eq. 1: Eq. 2: e) What is the coordinate of intersection? f) What does the intersection point mean in contet of the stor? g) If the decide to take this dream vacation in 3 ears right after high school graduation, who will have more mone towards the trip? How do we know? h) If the decide to go on the trip together when the turn 30, who will have had the better savings plan? How do we know? 21

22 Eample 3: John invests $20,000 into an account that earns 3.2% interest compounded quarterl. Rebecca invests $24,000 into an account that earns 2.4% interest compounded monthl. a) Define our variables: b)write our equations: c) Table: Pull up the table on our graphing d) Graph: Label aes, lines, calculator and find the 2 values intercepts and intersection point. between which the intersection occurs. : Eq. 1: Eq. 2: What is the maimum and value that we should use for our window? e) What is the coordinate of intersection? f) What does the intersection point mean in contet of the stor? g) Who has the better investment in the short term? Who has the better investment in the long term? HOMEWORK: Worksheet

23 ANSWERS TO SELECTED HOMEWORK QUESTIONS: 6-1: 1. = # of pizzas, =# of breadsticks 1a) + 2 = 0 1b) answers will var 3. = # adult tickets, = # child tickets 3a) + 6 = 60 3b) answers will var. = 34,000(1.0) tt : ON # 1-12, CHECK ALL GRAPHS WITH TEACHER! 1. (0, -3) 3. (2, -3). (2, -1) 7. (4, 2) 9. (0, 4) 11. No solution 13. (2, 1) 1. (1, 2) 17. infinite solutions 19. (-3, ) 6-3: 1. (-6, -8) 3. (4, -2). (2, -1) 7. (0, 2) 9. (-/6, 3) 11. (-1, /3) 13. (1,6) 1. (2, ) 17. infinite solutions 19. (4, 1 ½) 21. (8, -2) 23

24 6-4: : CHECK GRAPHS WITH TEACHER!!! 1. (3.2, -3.6) 3. (26.2, 12.). (0.30, 0.20) 7. (1.03, 2.26) 9. (0.8, 1.) 11. No solution 6-6: 1a) (30, 60) 1c) Store A 2a) (4., 0,000) 2c) Cit B 24

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