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Welcome back…. Let’s warm up!PowerPoint Presentation

Welcome back…. Let’s warm up!

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### 8-4 Elimination Using Multiplication

Objective: To solve systems of equations using the Elimination method with Multiplication

**Let’s use whiteboards today!

Example 1 – on paper

2x + y = 5

3x – 2y = 4

7x = 14

x = 2

2(2) + y = 5

4 + y = 5

y = 1

( ) 2

= 4x + 2y = 10

3x – 2y = 4

ANSWER: (2,1)

-2x + y = -6

Answers:

1. (2,-2)

2. (5,-2)

3. Infinitely Many

On a white board!!2) 3x – 2y = 19

5x + 4y = 17

3) x – 2y = -1

-2x + 4y = 2

Example 2 – on paper

0 = -y + 4

y = 4

3x = 2(4) – 2

3x = 8 – 2

3x = 6

x = 2

9x = 5y – 2

9x = 5y – 2

3x = 2y – 2

( ) -3

= -9x = -6y + 6

ANSWER: (2,4)

EXAMPLE 3 – on whiteboard

( )4

( )3

2x – 3y = 2

5x + 4y = 28

What do we eliminate?

y!

2(4) – 3y = 2

8 – 3y = 2

-3y = -6

y = 2

8x – 12y = 8

15x + 12y = 84

23x = 92

x = 4

ANSWER (4,2)

EX4: 2x + 3y = 5 5x + 4y = 16

Answer: (4,-1)

Eliminate x

1st times 5

2nd times -2

10x + 15y = 25

-10x – 8y = -32

7y = -7

y = -1

Eliminate y

1st times 4

2nd times -3

8x + 12y = 20

-15x – 12y = -48

-7x = -28

x = 4

Homework:

- Pg. 479 # 15 – 31 odd

-2x + y = -6

Answers:

1. (2,-2)

2. Infinitely Many

Elimination with Multiplication2) x – 2y = -1

-2x + 4y = 2

Elimination with Multiplication

1) 4x + 3y = 19

3x – 4y = 8

Answer: (4,1)

2) 4x – 7y = 10

3x + 2y = -7

Answer: (-1,-2)

Even More Practice

Solve using any method:

Shall we race??

1) 7x + 3y = -1

4x + y = 3

2) 3x + 4y = 10

6x + 8y = 5

3) x – y = 2

2x – 3y = 5

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