UNIT 5: Systems of Equations

Transcription

1 Algebra 2 Trig UNIT 5: Systems of Equations Name: Teacher: Pd: 1

2 Table of Contents Day 1: Review Solving Linear Systems SWBAT: Solve linear systems algebraically and graphically. Homework: Page 7 Day 2: Linear System Word Problems SWBAT: Solve word problems using linear systems of equations. Homework: Pages Day 3: 3 x 3 Linear Systems (Big Ideas 1.4) SWBAT: Solve systems of linear equations in three variables algebraically. Homework: Pages Day 4: Solving Word Problems Using a 3 x 3 Linear Systems (Big Ideas 1.4) SWBAT: Solve word problems using a 3 x 3 system. Homework: Page 22 **Homework answers follow each lesson** 2

3 SWBAT: Solve linear systems algebraically and graphically Day 1: Review Solving Linear Systems Do Now: Graph each of the lines on the set of axes below: y = 5x +1 and y = 2x- 11 Let s solve the same system algebraically. When finding the intersection of two lines from both Algebra I and Geometry, you first "set the linear equations equal" to each other. Find the intersection point of the two lines whose equations are shown below. Be sure to find both the x and y coordinates. y 5x 1 and y 2x 11 Explain why you cannot find the intersection points of the two lines shown below. Give both an algebraic reason and a graphical reason. y 4x 1 and y 4x 10 3

4 Systems of equations, or more than one equation, arise frequently in mathematics. To solve a system means to find all sets of values that simultaneously make all equations true. Of special importance are systems of linear equations. You have solved them in your last two Common Core math courses, but we will add to their complexity in this lesson. Examples: Solve the following system of equations by: (a) substitution and (b) by elimination. (a) 3x 2y 9 2x y 7 (b) 3x 2y 9 2x y 7 Example 1 Solve the system of equations algebraically using elimination: 3x +y = 4 6x + 2y = -4 4

5 Example 2 Solve the system of equations graphically: y = 2x -1 y = x Example 3 Solve the system of equations algebraically using substitution: y = -x + 2-5x +5y = 10 5

6 Example 4 Example 5 Example 6 6

7 Homework #1 Please complete all problems on a separate piece of paper Answer Key HW#1 7

8 Day 1 Homework Answers: 8

9 Day 2: Linear System Word Problems SWBAT: Solve word problems using linear systems of equations Do Now: Write each number in standard form 4) 60,000+ 5, ) 2, ) 1, Write the following in expanded form: 7) 52 8) 18 9) 70 10) xy 9

10 Model Problem: 10

11 Example 1: Example 2: Example 3: Model Problem with Current Application Example 4: 11

12 2 12

13 Answer Key: HW #2 13

14 Day 3: 3 x 3 Linear Systems Big Ideas 1.4 SWBAT: Solve systems of linear equations in three variables algebraically. Do Now: The sum of two numbers is 5 and the larger difference of the two numbers is 39. Find the two numbers by setting a system of two equations with two unknowns and solving the system algebraically. In this lesson we will extend the method of elimination to linear system of three equations and three unknowns. 14

15 Example 1: Consider the three-by-three system of linear equations shown below. Each equation is numbered in this first exercise to help keep track of our manipulations. Example 2: Solve the system of equations for x, y and z. 15

16 Example 3: Solve the system of equations for x, y and z. Example 4: Solve the system of equations for x, y and z. 16

17 Homework #

18 3. 4. Solve the system of equations algebraically. 18

19 5. Solve the system of equations algebraically. Answer Key HW#3:

20 Day 4: Solving word problems using a 3 x 3 system - Big Ideas 1.4 SWBAT to solve word problems using a 3 x 3 system. Do now: Read the following example. Find the three unknowns in the problem. Solve the system. Three orders are placed at a pizza shop. Two small pizzas, a liter of soda, and a salad cost $14; one small pizza, a liter of soda, and three salads cost $15; and three small pizzas, a liter of soda, and two salads cost $22. How much does each item cost? 1. The Arcadium arcade in Lynchburg, Tennessee uses 3 different colored tokens for their game machines. For $20 you can purchase any of the following mixtures of tokens: 14 gold, 20 silver, and 24 bronze; OR, 20 gold, 15 silver, and 19 bronze; OR, 30 gold, 5 silver, and 13 bronze. What is the monetary value of each token? 20

21 2. Last Tuesday, Regal Cinemas sold a total of 8500 movie tickets. Proceeds totaled $64,600. Tickets can be bought in one of 3 ways: a matinee admission costs $5, student admission is $6 all day, and regular admissions are $8.50. How many of each type of ticket was sold if twice as many student tickets were sold as matinee tickets? 3. Sam s furniture store places the following advertisement in the local newspaper. Write a system of equations for the three combinations of furniture. What is the price of each piece of furniture? 4. A stadium has 10,000 seats, divided into box seats, lower-deck seats, and upper- deck seats. Box seats sell for $10, lower-deck seats sell for $8, and upper-deck seats sell for $5. When all the seats for a game are sold, the total revenue is $70,000. The stadium has four times as many upper-deck seats as box seats. Find the number of lower-deck seats in the stadium. 21

22 HW# A wholesale store advertises that for $20 you can buy one pound each of peanuts, cashews and almonds. Cashews cost as much as peanuts and almonds combined. You purchase 2 pounds of peanuts, 1 pound of cashews and 3 pounds of almonds for $36. What is the price per pound of each type of nut? 3. The sum of three numbers is -4. The second number decreased by the third is the first. The sum of the first and second numbers is -5. Find the numbers. 22

23 Day 4 Homework Answer Key: almonds cost $6; peanuts cost $4 and cashews cost $10 3. The numbers are -3, -2 and 1. 23