Welcome back…. Let’s warm up!

1) 4x + 5y = 12 2) 3x – 2y = 12

4x + 3y = 4 4x + 2y = 2

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)

On a white board!!

1) -3x – 4y = 2

-2x + y = -6

Answers:

1. (2,-2)

2. (5,-2)

3. Infinitely Many

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

( ) -3 = -9x = -6y + 6

9x = 5y – 2

ANSWER: (2,4)

9x = 5y – 23x = 2y – 2

EXAMPLE 3 – on whiteboard

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)

( )4

( )3

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

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

Answer: (4,-1)

Try with a mathlete:

1) 3x + 5y = 11

2x + 3y = 7

2) 2x – 3y = 8

-5x + 2y = 13

Homework:

Pg. 479 # 15 – 31 odd

Math Lab

Systems of Equations Review

**Let’s use whiteboards today!

Substitution

1) y = 3x x + 2y = -21

Answers:1) (-3,-9)2) (3,0)

2) y = 2x – 6 3x + 2y = 9

Elimination

1) -3x + 4y = 12 2) x + y = 8

3x – 6y = 18 x – y = 4

(-24,-15) (6,2)

Elimination with Multiplication

1) -3x – 4y = 2

-2x + y = -6

Answers:

1. (2,-2)

2. Infinitely Many

2) 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