Elimination Exploring Linear Systems QUIZ ( ) Solving Problems with Systems of Equations. Distance/Velocity/Time Problems WS 1.

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1 UNIT 1 SYSTEMS OF LINEAR EQUATIONS Lesson TOPIC Homework Sept Sept Sept Sept Sept. 10 Sept. 11 Sept. 12 Sept. 13 Sept. 14 Sept. 17 Sept. 18 Sept Getting Ready WS 1.0 ARE YOU READY FOR THIS? Fill in Info sheet and get permission sheet signed. Bring in $2 for lesson shells & $7 if you need a calculator Representing Linear Relations Pg. 12 # 1, 4, 5, 9, 13, 15 WS 1.1 Solving Systems of Equations Graphically Solving Systems of Equations by Substitution Solving Systems of Equations by Elimination Exploring Linear Systems QUIZ ( ) Solving Problems with Systems of Equations Pg. 26 # 1, 2, 5, 10, 14, 17ab Pg. 38 # 1 5, 10, 12, 16 Pg. 54 # 1, 2, 4, 6, 11bdf Pg. 59 # 1, 2, 3abgh, 5, 6 WS 1.6 # 1 10 Distance/Velocity/Time Problems WS 1.6 # 11, 12, Mixture Problems QUIZ ( ) WS 1.6 # Break Even Problems WS 1.9 # 1-5 Review for Unit 1 Test Pg. 62 # 2 9, 10ac, TEST- UNIT 1

2 MPM 2D Lesson 1.1 Representing Linear Relations Ex. 1 Translate Words Into Algebra a) Write each phrase as a mathematical expression: i) the value five increased by a number ii) seven less than twice a number b) Write the following sentence as a mathematical equation. i) Half of a value, decreased by seven, is one. ii) Twice a number, subtracted from five, is three more than seven times the number. c) Translate the following sentence into an equation, using two variables. i) Mario s daily earnings are $80 plus 12% commission on his sales. ii) Fitness Club CanFit charges a $150 initial fee to join the club and a $20 monthly fee. Ex. 2 Does the point ( 3, 2) satisfy the linear relation 2x 3y 12 0?

3 Ex. 3 Brian and Catherine want to get Internet access for their home. There are two companies in the area. IT Plus charges a flat rate of $25/month for unlimited use. Techies Inc. charges $10/month plus $1/h. If Brian and Catherine expect to use the Internet for approximately 18 h/month, which plan is the better option for them? Determine the two equations you would use to solve the problem. Ex. 4 Ali owns a small airplane. He pays $50/h for flying time and $300/month for hangar fees at the local airport. If Ian rented the same type of airplane at the local flying club, it would cost him $100/h. How many hours will Ali have to fly each month so that the cost of renting will be the same as the cost of flying his own plane? Determine the two equations you would use to solve the problem. Pg. 12 # 1, 4, 5, 9, 13, 15 WS 1.1

4 MPM 2D Lesson 1.2 Solving Systems of Equations Graphically Ex. 1 Solve by using tables of values (ToV). 2x + y = y = x y x x y = 3 2 x x Ex. 2 Solve by using x and y intercepts. 3x + 2y = x 2y = y x

5 Ex. 3 Find the slope and the y-intercept of each of the following linear relations. a) 3x + 2y = 9 b) 2x 5y = 20 Ex. 4 Solve by using the slope and the y intercept. 3x + y = x + 3y = y x Ex. 5 Determine whether or not ( 3, 2) is a solution to the given system. 3x + 2y = x + y = Pg. 26 # 1, 2, 5, 10, 14, 17ab

6 MPM 2D Lesson 1.3 Solving Systems of Equations by Substitution Ex. 1 Solve using the method of substitution and check your answer. 5x 2y x 2y You do not always have to rearrange for a variable. Sometimes it is easier to rearrange for a multiple of a variable the sub it in to the other equation. Always explain each step before you do it. Ex. 2 Marla and Nancy played in a volleyball marathon for charity. They played for 38 h and raised $412. Marla was sponsored for $10/h and Nancy was sponsored for $12/h. How many hours did each play?

7 Ex. 3 Sarah is starting a business in which she will hem pants. Her start up cost, to buy a sewing machine, is $1045. She will use about $0.50 in materials to hem each pair of pants. She plans to charge $10 for each pair of pants she hems. How many pairs of pants does she need to hem to break even? Pg. 38 # 1 5, 10, 12, 16

8 MPM 2D Lesson 1.4 Solving Systems of Equations by Elimination To solve a system by elimination, decide which variable to eliminate to eliminate a variable, it must have the same numerical coefficient in both equations to eliminate, either add or subtract the equations based on the signs of the variable o if signs are the same, subtract ie: -3 (-3) = 0 o if signs are different, add ie: -3 + (3) = 0 continue to solve for the variables as you have previously Ex. 1 Solve each system of equations. a) 7x 4y = b) 8x - 4y = x + 2y = x - 3y =

9 Ex. 2 Solve each of the following systems of equations algebraically using any method you wish. a) x 3y x 9y b) 2(2x 1) ( y 4) (1 x) 2( y 3) 6 ---

10 Ex. 3 Every day at her bakery, Brenna bakes chocolate chip cookies and oatmeal cookies. She uses different amounts of butter and oatmeal in each recipe. Each batch of chocolate chip cookies uses 13 kg of butter and 8 kg of oatmeal while each batch of oatmeal cookies uses 2 kg of butter and 29 kg of oatmeal. If she has 47 kg of butter and 140 kg of oatmeal, how many batches of each type of cookie does she bake? Pg. 54 # 1, 2, 4, 6, 11bdf

11 MPM 2D Lesson 1.5 Exploring Linear Systems How many possible ways can two lines intersect? y x y x y x

12 Ex. Determine the number of intersections for each of the following systems of equations. a) y 3x y 5x 1--- b) y 2x 3--- y 2x c) 2x 3y x 6y d) 5x 2y x 2y Pg. 59 # 1, 2, 3abgh, 5, 6

13 MPM 2D Lesson 1.6 Solving Problems with Systems of Equations Algorithm Determine the 2 unknown quantities by reading the question thoroughly and carefully. Introduce a variable for each unknown. Construct two equations using both variables in each. Solve the system and check your answer. Answer the problem with a statement. Ex. 1 The larger of two numbers multiplied by five increased by three times the smaller number is 129. Nine times the smaller number decreased by twice the larger is 81. Find the numbers. Ex. 2 Two numbers have a difference of 123. The larger is 22 more than twice the smaller. Find the numbers.

14 Ex. 3 Sam has $113 made up of $2 coins and $5 bills. If there are 31 bills and coins, how many $2 coins are there? Ex. 4 A parking metre contained 78 coins made up of dimes and nickels. If there is $5.20, how many of each type of coin are there? WS 1.6 # 1-10

15 MPM 2D Lesson 1.7 Distance/Velocity/Time Problems Ex. 1 It is 395 km from Ski Valley to Vancouver. Ivy made the trip in 6 h, traveling by bus and by train. The train averaged 70 km/h and the bus 60 km/h. How much time did she spend on the train?

16 Ex. 2 Evangeline drove 500 km from Windsor to Peterborough 5 h 30 min. She drove part of the way at a steady speed of 100 km/h and the rest of the way at 80 km/h. How far did she travel at each speed? WS 1.6 # 11, 12, 14 17

17 MPM 2D Lesson 1.8 Mixture Problems Ex. 1 Jelly Beans worth $2.10/kg and mints worth $2.70/kg are mixed to make 500 kg of a mixture which is sold for $2.52/kg. How many kg of mints are used? Ex. 2 Pierre invested $6000, part at 7.5%/a and the rest at 8.5%/a. The interest after 1 year is $470. How much was invested at each rate?

18 Ex. 3 How many kilograms of 30 % salt solution and 40% salt solution should be mixed to form 200 kg of a 37% salt solution? WS 1.6 # 18-23

19 MPM 2D Lesson 1.9 Break Even Problems Ex. 1 To send a package from any city in Ontario to any other city in Ontario, Fast Express charges $5 plus $1/kg. For the same service Tomorrow Delivery charges $3.50 plus $1.25/kg. a) Write a linear system that models this situation. b) Solve the system algebraically. c) When will the cost of delivery be the same for both companies? e) If a package weighs 5 kg, which company would you use?

20 Ex. 2 Zaria wants to open a chequing account. Maple Savings charges $6/month plus $0.75/cheque. Ontario Trust charges $8/month plus $0.50/cheque. a) Write a linear system that models this situation. b) Solve the system algebraically. c) When will the cost of cheques be the same for both banks? d) If she writes 20 cheques per month, which bank should she use? WS 1.9 # 1-5