Name ___________________________________________ Class Period ________

Secondary 1 Honors

Unit 6 ~ Systems of Equations

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Schedule for Unit 6 A-Day B-Day What we’re doing Assignment What is

due? Jan. 11 Jan. 12 6-1: Graph Inequalities & Write

Equations

6-1

Jan. 13 Jan. 17 6-2: Graphing Systems of Equations & Solving by Substitution

WS 6-2 6-1

Jan. 18 Jan. 19 6-3: Solving by Elimination

6-3 WS 6-2

Jan. 20 Jan. 23

Quiz 6-2,3 6-4: Systems of Inequalities

WS 6-4 6-3

Jan. 24 Jan. 25 Quiz 6-4 6-5: Systems on the Graphing Calculator

WS 6-5 WS 6-4

Jan. 26 Jan. 27 Quiz on 5-4 6-6: Systems in Context

WS 6-6 WS 6-5

Jan. 30 Jan. 31 Review

Review WS WS 6-6

Feb. 1 Feb. 2 Unit 6 Test

Review WS

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NOTES 6-1: Graphing Inequalities & Writing Equations

Check whether the given ordered pair is a solution of 𝟐𝟐𝟐𝟐 + 𝟑𝟑𝟑𝟑 ≥ 𝟓𝟓. Ex 1: (0, 1)

Ex 2: (4, -1) Graphing a Linear Inequality. Step 1: Step 2: Step 3:

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Graph the following inequalities in a coordinate plane. Ex 3: 𝑦𝑦 < −2 Ex 4: 𝑥𝑥 ≤ 1 Ex 5: 𝑦𝑦 < 2𝑥𝑥 + 3 Ex 6: 2𝑥𝑥 − 5𝑦𝑦 ≥ 10

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Ex. 7: You and your family have gone to a football game. Your mom sends you to the concession stand to get food for everyone. 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 you could have purchased. Ex. 8: You open a savings account with $500. The bank tells you that they will give you an interest rate of 3.5% annually. Write an equation to represent this situation. Ex. 9: You start a hike with your friends 10 miles away from home. You and your group hike at a rate of 6 miles per hour. Write an equation to represent this situation.

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HW 6-1: Graphing Inequalities & Writing Equations Instructions: You do NOT need to write out the entire story problem, but you DO need to define any variables that you use, and be sure that you do all parts.

1. When you go to Little Caesar’s to buy food for a family party, you find out they charge $5 for each pizza and $2 for an order of breadsticks. You spend $50 on the food (before tax).

a. Write an equation to represent this situation. b. List three different combinations of pizza and breadsticks you could have purchased.

2. You purchase a car for $6000. The car depreciates in value by 8% each year. 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 $10 for each adult ticket and $6.00 for each child ticket. You spent $60 on the tickets (before tax).

a. Write an equation to represent this situation.

b. List three different combinations of child and adult tickets you 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 day. Write an equation to represent this situation.

5. The city of Pythagoras started with a population of 34,000 people. The city was growing at a rate of 5% each year. 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 $5 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 inequality. Use the graph paper at the end of the packet, and attach it to your other work.

7. 3y > −

8. 34

y x≤

9. 3 0x y+ ≤

10. 7 24

y x≥ +

11. 1x ≥

12. 7 3 9x y− ≥

13. 1 55

y x> − −

14. 4 4x y+ ≥ −

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Notes 6-2: Solving Systems of Equations using Graphing & Substitution

• Systems of Two Linear Equations:

• A Solution to a System of Equations:

Solve the system using a graph.

Ex. 1: 12 2

y xy x= −

= −

-5 5

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5

x

y

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Ex. 2: 43

y xy x=

= +

Ex. 3: 2 23x

y xy= +

=

Ex. 4: 3 22

x yx y

+ = − =

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Steps for Substitution Method:

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

Solve the system of equations using substitution.

Ex. 5: 3 84

y xy x= −

= −

Ex. 6: 2 6

y xx y= −

− + = −

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Solve the system of equations using substitution.

Ex. 7: 2 3 52 17x y

x y+ =

− + = −

Ex. 8: 2 2 34 1

x yx y

+ = − = −

Ex. 9: 5 5 222

x yx y− + =

− =

HOMEWORK: WORKSHEET 6-2 10

Notes 6-3: Solving Systems of Equations using Elimination

Warm-up:

Find the solution to the system of equations.

1. 2.

3.

STOP HERE & WAIT!

Zero Pairs:

What does it take to add up to zero?

Ex. 1: Ex. 3:

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Common Denominators:

What is the common denominator for the given fractions?

Ex. 3: Ex. 5:

Ex. 6:

Elimination Method

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

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Solve the system of equations using elimination.

Ex. 7:

Ex. 8:

Ex. 9:

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Solve each system of equations by elimination.

Ex. 10:

Ex. 11:

Ex. 12:

Ex. 13:

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HW 6-3: Solving Systems of Equations Using Elimination

For questions #1-12, solve using elimination. SHOW ALL WORK! Remember you can check your solutions!

1. 2. 3.

4. 5. 6.

7. 8. 9.

10. 11. 12.

For questions #13-21, solve using any method you choose. Use graph paper at the end of the packet IF you solve by graphing.

13. 14. 15.

16. 17. 18.

19. 20. 21.

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Notes 6-4: Solving Systems of Linear Inequalities

Check whether the given ordered pair is a solution of 𝟐𝟐𝟐𝟐 + 𝟑𝟑𝟑𝟑 ≥ 𝟓𝟓. Ex 1: (0, 1) Ex 2: (4, -1)

Ex 3: (2, 1)

Graphing a System of Linear Inequalities. Step 1: Step 2: Step 3:

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Graph the following inequalities in a coordinate plane. Ex 4: 3 1

2y xy x≥ − −

< +

Ex 5: 2 33 4

x yy x− ≤

> −

Ex 6: 32

yx<

> −

Ex 7: 2 42 3

x yx y− >

− < −

HOMEWORK: Worksheet 6-4

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Notes 6-5: Solving Systems on a Graphing Calculator

Example 1: Use a graphing calculator to determine the best window to view the solution to the system of equations. Draw a quick sketch of the system in a standard window and in the best window. (Make sure you draw your axes and label your min and max for each axis.) a. b.

1 92

2 53

y x

y x

= − +

= − +

( )

( )

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2 13

x

f x

g x x

=

= − +

Standard Window: Standard Window: Best Window: Best Window: Example 2: Use the two systems of equations above and your graphing calculator to solve the system. (Find the point(s) of intersection.) Write the solution below and label it on your graph above. Round the answers to the hundredths place, if necessary. a. b.

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HOMEWORK: Worksheet 6.5

Notes 6-6: Systems of Equations in Context

Provide the desired information about each situation given. You may use your graphing calculator to find the graph and table of the information.

Example 1: You are having some friends over for a party this weekend at your house. Your parents have said you have $60 that you can spend on food, and you’ve decided to use that money to buy pizzas and ice cream. Macey’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 your variables:

b) Write your equations:

c) Graph: Label axes, lines, intercepts and d) Table: Must go from y-intercept intersection point. to x-intercepts and include WHOLE # VALUES.

e) What is the coordinate of intersection?

Equation 1:

Ordered Pairs

Equation 2:

Ordered Pairs

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f) What does the intersection point mean in context of the story?

g) If you decide to spend all of your money on pizza, which store should you choose? Why? How does this decision show up on the graph?

h) If you decide that you need to buy 7 pizzas, which store will allow you to buy more ice cream on your budget? How does this decision show up on the graph?

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Example 2: Addie and Ben are 15 years old and are in 9th grade right now. They decide to start saving up their money to take a dream vacation one day. Addie puts $500.00 into a savings account and decides to deposit $45.00 into this special savings account every year. Ben puts $450.00 into a savings account and plans to just get more money off of the interest he will earn. His account earns 7.5% interest compounded annually.

a) Define your variables:

b) Write your equations:

c) Graph: Label axes, lines, intercepts and d) Table: Include x values from 0 – 15. intersection point.

e) What is the coordinate of intersection?

f) What does the intersection point mean in context of the story?

g) If they decide to take this dream vacation in 3 years right after high school graduation, who will have more money towards the trip? How do we know?

h) If they decide to go on the trip together when they turn 30, who will have had the better savings plan? How do we know?

:

Eq. 1: Eq. 2:

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Example 3:

John invests $20,000 into an account that earns 3.2% interest compounded quarterly.

Rebecca invests $24,000 into an account that earns 2.4% interest compounded monthly.

a) Define your variables: b)Write your equations:

c) Table: Pull up the table on your graphing d) Graph: Label axes, lines, calculator and find the 2 x values intercepts and intersection point.

between which the intersection occurs.

What is the maximum x and y value that we should use for our window?

e) What is the coordinate of intersection?

f) What does the intersection point mean in context of the story?

g) Who has the better investment in the short term? Who has the better investment in the long term?

HOMEWORK: Worksheet 6-6

:

Eq. 1: Eq. 2:

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ANSWERS TO SELECTED HOMEWORK QUESTIONS:

6-1: 1. x = # of pizzas, y=# of breadsticks 1a) 5𝑥𝑥 + 2𝑦𝑦 = 50 1b) answers will vary

3. x= # adult tickets, y = # child tickets 3a) 10𝑥𝑥 + 6𝑦𝑦 = 60 3b) answers will vary

5. 𝑦𝑦 = 34,000(1.05)𝑡𝑡

7. 9. 11.

13.

6-2: ON # 1- 12, CHECK ALL GRAPHS WITH TEACHER!

1. (0, -3) 3. (2, -3) 5. (2, -1) 7. (4, 2)

9. (0, 4) 11. No solution 13. (2, 1) 15. (1, 2)

17. infinite solutions 19. (-3, 5)

6-3: 1. (-6, -8) 3. (4, -2) 5. (2, -1) 7. (0, 2)

9. (-5/6, 3) 11. (-1, 10/3) 13. (1,6) 15. (2, 5)

17. infinite solutions 19. (4, 1 ½) 21. (8, -2)

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6-4:

1. 3. 5.

7. 9. 11.

13. 15. 17.

6-5: CHECK GRAPHS WITH TEACHER!!!

1. (3.2, -3.6) 3. (26.25, 12.5) 5. (0.30, 0.20)

7. (1.03, 2.26) 9. (0.58, 1.5) 11. No solution

6-6: 1a) (30, 60) 1c) Store A 2a) (4.5, 50,000) 2c) City B

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