Over Lesson 6–1

• "If a team is to reach its potential, each player must be willing to subordinate his personal goals to the good of the team."

~ Bud Wilkinson

• Turn and Talk to a peer about this quote and its relevancy to your own work. What does this mean to you?

• Each team must have at least one representative to respond.

Over Lesson 6–1

Save the Date

1st Exchange Email and Numbers

Due today: Launch and Brainstorm (Choose a Point Person)

Launch: Bullets 1 – 3 Assign a member to oversee 5 roles. Discuss and turn in ideas for each. Write your role(s) and responsibilities in your notebook.

• (1) Venue - Choose a location for at least 50 people - Real location• (2) Catering – Choose a caterer to provide a 4 course meal - Real

location• (3) Decorations and Favors – A gift should be provided at each

place setting. Have a picture and provide a vivid description.

Each person should compare costs and minimum purchase amounts. If you are assigned to find a venue and do the catering, members should - Research local companies online and contact businesses to get their fees.

Over Lesson 6–1

"Coming together is a beginning. Keeping together is progress. Working together is success. "

~ Henry Ford

Due Wednesday March 12• Task 1: #1 on the Fundraising Guidelines

Research and describe the cause for the charity and theme.

• Task 2 – (4th person) Members should research careers as an event planner, including a job description and qualifications (Include this in your project).

Over Lesson 6–1

• "Teamwork divides the task and multiplies the success. "

~ Unknown • All students in each group should research and

understand the terms costs, revenues and profits. Tell what will be included in each for your project. (Include in your project)

• (5) Also, find and choose an organization that you will donate proceeds to. (Choose a member to oversee)

• Write on the same paper as yesterday.

Over Lesson 6–1

• Brainstorm: Today, think about a theme for the fundraising dinner. Come to a decision as a group so that the details can be based around a theme. (Grab a handout)

You solved systems of equations by graphing.

• Solve systems of equations by using substitution.

• Solve real-world problems involving systems of equations by using substitution.

3 METHODS TO SOLVE A SYSTEM OF EQUATIONS

1.BY GRAPHING (Lesson 6-1) √2.BY SUBSTITUTION (Lesson 6-2)3.BY ELIMINATION – a. with Addition and Subtraction

(Lesson 6-3) b. with Multiplication (Lesson 6-4)

Over Lesson 6–1

Use substitution to solve the system of equations.

1. What is the solution to the system of equationsy = 2x + 1 and y = –x – 2?

2. Adult tickets to a play cost $5 and student tickets cost $4. On Saturday, the adults that paid accounted for seven more than twice the number of students that paid. The income from ticket sales was $455. How many students paid?

• Do Packet 5 - 7

• Do Packet 5 - 7

Solve and then Substitute

Use substitution to solve the system of equations.4x + 5y = 11

y – 3x = -13

Step 1 Solve the first equation for y since thecoefficient is -1.

Use substitution to solve the system of equations.3x – y = –12–4x + 2y = 20

• Do Packet 17, 18

No Solution or Infinitely Many Solutions

Use substitution to solve the system of equations.2x + 2y = 8x + y = –2

Solve the second equation for y.

x + y = –2Second equation

x + y – x = –2 – xSubtract x from each side.

y = –2 – xSimplify.

Substitute –2 – x for y in the first equation.

2x + 2y = 8First equation

2x + 2(–2 – x) =8 y = –2 – x

No Solution or Infinitely Many Solutions

2x – 4 – 2x = 8Distributive

Property –4= 8Simplify.

The statement –4 = 8 is false. This means that there are no solutions of the system of equations.

If a system results in a false sentence such as -4 = 8, then the system has no solution. The equations represent parallel lines.

Answer: no solution

Use substitution to solve the system of equations.3x + y = -56x + 2y = 10

If a system results in a true sentence, then the system has infinitely many solutions. This happens when 2 equations are the same line.

Write and Solve a System of Equations

NATURE CENTER A nature center charges $35.25 for a yearly membership and $6.25 for a single admission. Last week it sold a combined total of 50 yearly memberships and single admissions for $660.50. How many memberships and how many single admissions were sold?

Let x = the number of yearly memberships, and let y = the number of single admissions.

So, the two equations are x + y = 50 and35.25x + 6.25y = 660.50.

Write and Solve a System of Equations

Step 1 Solve the first equation for x.

x + y = 50First

equation

x + y – y = 50 – y Subtract y from each side.

x = 50 – ySimplify.

Step 2 Substitute 50 – y for x in the second equation.

35.25x + 6.25y =660.50Second

equation

35.25(50 – y) + 6.25y =660.50Substitute 50 – y for x.

Write and Solve a System of Equations

1762.50 – 35.25y + 6.25y =660.50Distributive Property

1762.50 – 29y =660.50Combine

like terms.

–29y = –1102 Subtract 1762.50 from each side.

y = 38Divide each side by –29.

Write and Solve a System of Equations

Step 3 Substitute 38 for y in either equation to find x.

x + y = 50First

equation

x + 38 = 50Substitute

38 for y.

x = 12Subtract 38 from each side.

Answer: The nature center sold 12 yearly memberships and 38 single admissions.