complete the literature analysis from monday. use the resources on the internet and each other to...

Opener

Complete the Literature Analysis from Monday.

Use the resources on the internet and each other to help you relearn the concept.

Use whiteboards.Use laptops.Work together.

3.2 Solving Linear Systems by “Elimination”

SWBAT solve a system of 2 linear equations by using the process of elimination.

Write down the date, Section #, Title and Learning Objective(s) into your notebook.

Key ConceptsLOOK LISTEN

Write into “Key Concepts” as you Look & Listen.

1. “Ax + By = C”2. Choose one of the variables to “eliminate:” 3. Multiply either both eqs. or one, by a number that will

give the LCM. 4. Now combine and solve twice: once for the

“eliminated” variable and then for the remaining variable.

How do I solve by using “Elimination?”

Key ConceptsLOOK LISTEN

Write down into “Key Concepts” as you Look & Listen.

Solution Exists 0 = 0 True Statement

0 # False Statement

• Intersecting lines have one solution

• System has solution

• Coincident lines have infinite solutions.

• Both variables cancel out 0=0 True statement

• Parallel lines have no solutions.

• Both variables cancel out 0 = # False Statement

1 2m m 1 2 1 2,m m b b 1 2 1 2,m m b b

How do we get there?

SWBAT will be able to solve a 2 by 2 system using the process of elimination.

LOOK LISTEN

2 3 12

3 6

x y

x y

Multiply by 2

Choose x! Why?

2 3 12x y

Keep the “A” the same.

2 6 12x y

0

9 0

y

y

How do we get there?

SWBAT will be able to solve a 2 by 2 system using the process of elimination.

LOOK LISTEN

Determine if the system has one solution, an infinite number of solutions, or no solutions. Justify your answer. Do not solve or graph.

3 2

5 2 2

y x

x y

7 6

3 21 18

x y

x y

54

21

5 24

x y

x y

Now let’s try together.Use whiteboards.

SWBAT will be able to solve a 2 by 2 system using the process of elimination.

Determine if the system has one solution, an infinite number of solutions, or no solutions. Justify your answer. Do not solve or graph.

3 13

2 4

y x

x y

3 2 15

25

3

x y

x y

3 2

3 2

y x

y x

Now let’s try together.Use whiteboards.

SWBAT will be able to solve a 2 by 2 system using the process of elimination.

Determine if the system has one solution, an infinite number of solutions, or no solutions. Justify your answer. Do not solve or graph.

6 15 12

2 5 9

x y

x y

12 3 9

4 3

x y

x y

12 2 21

3 12 4

x y

x y

Now you try.Use your notebooks.

SWBAT will be able to solve a 2 by 2 system using the process of elimination.

Determine if the system has one solution, an infinite number of solutions, or no solutions. Justify your answer. Do not solve or graph.

6 2 5

3 7

x y

x y

2 5 7

4 2

x y

x y

4 3 10

8 6 20

x y

x y

Key ConceptsLOOK LISTEN

Write into “Key Concepts” as you Look & Listen.

• Take out a piece of paper and fold it into thirds lengthwise.

• Title the columns: 1 solution, infinite solutions and no solutions.

• Take the examples that we have done, and place them into the correct column.

Now make a conjecture. How can you simply look at the system and determine (write your answer at the bottom of the paper):• How many intersection points, if any?• How many solutions, if any?

How do we get there?

SWBAT will be able to solve a 2 by 2 system using the process of elimination.

LOOK LISTEN

3 7 10

6 8 8

x y

x y

Multiply by -2. Why?

Choose x! Why?

6 8 8x y

Keep the “B” the same.

6 14 20x y

6 12

2y

y

How do we get there?

SWBAT will be able to solve a 2 by 2 system using the process of elimination.

LOOK LISTEN

3 6 9

4 7 16

x y

x y

Multiply by 4. Why?

Choose x! Why?

12 21 48x y

Both equations change by the multiplier.

12 24 36x y

3 1

4

2y

y

Multiply by 3. Why?

Key ConceptsLOOK LISTEN

Write into “Key Concepts” as you Look & Listen.

1. “Ax + By = C”2. Choose one of the variables to “eliminate:” 3. Multiply either both eqs. or one, by a number that will

give the LCM. 4. Now combine and solve twice: once for the

“eliminated” variable and then for the remaining variable.

How do I solve by using “Elimination?”

Now let’s try together.Use whiteboards.

SWBAT will be able to solve a 2 by 2 system using the process of elimination.

6 4 14

2 8 21

x y

x y

Now let’s try together.Use whiteboards.

SWBAT will be able to solve a 2 by 2 system using the process of elimination.

8 9 15

5 2 17

x y

x y

Now let’s try together.Use whiteboards.

SWBAT will be able to solve a 2 by 2 system using the process of elimination.

4 5 13

6 2 48

x y

x y

Now you try.Use your notebooks.

SWBAT will be able to solve a 2 by 2 system using the process of elimination.

3 7 1

2 3 6

x y

x y

Now you try.Use your notebooks.

SWBAT will be able to solve a 2 by 2 system using the process of elimination.

4 3 8

8 6 16

x y

x y

Now you try.Use your notebooks.

SWBAT will be able to solve a 2 by 2 system using the process of elimination.

12 3 9

4 3

x y

x y