Created for Teacher Use LEARNING OBJECTIVE We will

Created for Teacher Use

LEARNING OBJECTIVE We will learn how to model 1 with Linear Systems 2. CFU What are we going to learn today? Definition Declare the Objective A: Read the Objective to B. B: Define Systems and Inequalities to A 1 2 Represents real-world situations and use them to solve problems. A set of two or more equations with same variables. Created for Teacher Use

We will learn how to model with Linear Systems. Solve the system. 1. Lisa spends part of her year as a member of a gym. She then finds a better deal at another gym, so she cancels her membership with the first gym after x months and spends the rest of the year, y months, with the second gym. Write the equation: x + y = 12 2 A company has to buy computers, x, and printers, y. They buy total of 19 machine. Write the equation: Make the Connection Students, you already know how to represent the equation using variables. Now, we are going to learn how to model with Linear Systems. x + y = 19 Created for Teacher Use

We will learn how to model with Linear Systems. A linear system can be used to model a real world problem when two equations can be created. Angie’s Awesome cupcakes sells designer cupcakes. Jagpal bought some chocolate and some vanilla for a total of 20 cupcakes. Chocolate cupcakes cost $5 and vanilla cupcakes cost $3. It was $84 for the 2 o cupcakes. The first equation is for the total number of machines. {TOTAL} x + y = 20 The second equation is for the total cost of the machines. {COST} Check for Understanding A PE teacher needs basketballs and volleyballs. She bought a total of 40 balls. Basketballs cost $7 each and volleyballs cost $5 each with a total spent of $230. Which linear system models the situation? How do you know? A. b + v = 40 7 b + 5 v = 230 B. b + v = 230 7 b + 5 v = 40 5 x + 3 y = 20 Created for Teacher Use

We will learn how to model with Linear Systems. CONCEPT DEVELOPMENT Write a system of equations to represent the situation, then solve the system A company has to buy computers and printers. Each computer, x, costs $525 costs $595 and each printer, y, costs $335. If the $370. If the company spends $9, 055 company spends $7, 125 and buys a total of 19 machines, how many of each did it buy? 595 x + 370 y = 9, 055 x + y = 19 595 x + 370 y = 9, 055 + − 595 x + − 595 y = − 11, 305 − 225 y = − 2, 250 y = 10 x + y = 19 x + 10 = 19 x=9 *Multiply by − 525 So, the company bought 9 computers and So, the company bought 4 computers 10 printers. and 15 printers. Created for Teacher Use

SKILL DEVELOPMENT / GUIDED PRACTICE We will learn how to model with Linear Systems. 1. Lisa spends part of her Write the system of equations only year as a member of a gym. Jack is selling tickets to an She then finds a better deal at event. Attendees can either buy Number of months another gym, so she cancels a general admission ticket, x, or x + y. y The = 12 her membership with the first a VIP ticket, general gym after x months and admission C tickets are $60 and os t spends the rest of the VIP tickets are $75. He does year, y months, with the 50 ymany = $720 not 65 x know+how of each second gym. The type he has sold, but he knows membership to the first gym he sold a total of 29 tickets and cost $65, while the made $1, 965. Write the system membership for the second only: gym cost $50. She ended up Check for a Understanding spending total of $720 over the course the Write B Explain to A: of How doyear. you write the system of equations? the system only: Created for Teacher Use

SKILL DEVELOPMENT / GUIDED PRACTICE We will learn how to model with Linear Systems. 1. A student has to buy graph paper and printer paper. The graph paper, x, costs $4, while the printer paper, y, costs $3. She wants to buy at least 5 packs of paper but wants to spend at most $17. Write the The student may purchase 5 or system: more packs of paper. x + y ≥ 5 $17 is the spending limit, so the cost must be less than or equal to it. $4 x + $3 y ≤ 17 Check for Understanding B Explain to A: How do you write the systems of inequalities? Anthony is buying towels for his apartment. He finds some green towels, x, that cost $5 each and at least ≥ blue towels, y, that cost $8 each. at most ≤ He wants to buy at least 5 towels, but does not want to spend more than $41. How many of each towel can he purchase? Write themay system: Angelique purchase 5 or more towels. x+y≥ 5 $41 is the spending limit, so the cost must be less than or equal to it. 5 x + 8 y ≤ 41 Created for Teacher Use

We will learn how to model with Linear Systems. 1 Solve the inequality for y (y = mx + b). 2 Graph the boundary line for the inequality. (< > ). 3 Shade the region (>, ³: Above, <, £: Below). 4 Shade Repeat the steps 1 -3 for second inequality. 5 region thatthe overlap. , £, ³ SKILL DEVELOPMENT / GUIDED PRACTICE 1. Graph of the system of inequalities. y-Intercept (0, b) = . overlap. Check for Understanding A: How do you determine what side to shade? B: How do you determine the final solution area? Remember the Concept . . . + Check for Understanding B Explain to A: How do you graph the systems of inequalities? Created for Teacher Use

We will learn how to model with Linear Systems. SKILL DEVELOPMENT / GUIDED PRACTICE 1 Solve the inequality for y (y = mx + b). 2 Graph the boundary line for the inequality. (< > ). 3 Shade the region (>, ³: Above, <, £: Below). 4 Shade Repeat the steps 1 -3 for second inequality. 5 region thatthe overlap. , £, ³ Check for Understanding A: How do you determine what side to shade? B: How do you decide where to do the final shade? 1. Graph of the 2 Graph of the system of inequalities. Remember the Concept overlap. Created for Teacher Use

SKILL DEVELOPMENT / GUIDED PRACTICE We will learn how to model with Linear Systems. 1. Lisa spends part of her Jack is selling tickets to an year as a member of a gym. event. Attendees can either buy She then finds a better deal at a general admission ticket, x, or Number of months another gym, so she cancels a VIP ticket, y. The general x +tickets y = 12 her membership with the first admission are $60 and gym after x months and the VIP tickets are $75. He does Cosmany t of each spends the rest of the not know how year, y months, with the type he has sold, =but he knows 65 x + 50 y $720 second gym. The he sold a total of 29 tickets and membership to the first gym made $1, 965. Write and Solve cost $65, while the system: membership for the second gym cost $50. She ended up Check for a Understanding spending total of $720 over the course the Write B Explain to A: of How doyear. you write the system of equations? and Solve system: Created for Teacher Use

SKILL DEVELOPMENT / GUIDED PRACTICE We will learn how to model with Linear Systems. 1. A student has to buy graph paper and printer paper. The graph paper, x, costs $4, while the printer paper, y, costs $3. She wants to buy at least 5 packs of paper but wants to spend at most $17. Write & The student may purchase 5 or Solve the system: more packs of paper. x + y ≥ 5 $17 is the spending limit, so the cost must be less than or equal to it. $4 x + $3 y ≤ 17 Check for Understanding B Explain to A: How do you write the systems of inequalities? Anthony is buying towels for his apartment. He finds some green towels, x, that cost $5 each and at least ≥ blue towels, y, that cost $8 each. at most ≤ He wants to buy at least 5 towels, but does not want to spend more than $41. How many of each towel can he purchase? Write & Solve the system: Angelique may purchase 5 or more towels. x+y≥ 5 $41 is the spending limit, so the cost must be less than or equal to it. 5 x + 8 y ≤ 41 Created for Teacher Use

SUMMARY CLOSURE We will learn how to model with Linear Systems. What did you learn today about how to Word Bank model with Linear Systems Created for Teacher Use

We will learn how to model with Linear Systems. INDEPENDENT PRACTICE 1 Created for Teacher Use