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Welcome back….
Let’s warm up!
1) 4x + 5y = 12
4x + 3y = 4
2) 3x – 2y = 12
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 ) 2 = 4x + 2y = 10
3x – 2y = 4
3x – 2y = 4
7x
2(2) + y = 5
4+y=5
y=1
= 14
x=2
ANSWER: (2,1)
On a white board!!
1) -3x – 4y = 2
-2x + y = -6
2) 3x – 2y = 19
5x + 4y = 17
3) x – 2y = -1
-2x + 4y = 2
Answers:
1. (2,-2)
2. (5,-2)
3. Infinitely
Many
Example 2 – on paper
9x = 5y – 2
9x = 5y – 2
( 3x = 2y – 2 ) -3 = -9x = -6y + 6
0 = -y + 4
y=4
3x = 2(4) – 2
3x = 8 – 2
ANSWER: (2,4)
3x = 6
x=2
EXAMPLE 3 – on whiteboard
( 2x – 3y = 2 )4
( 5x + 4y = 28)3
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
Eliminate y
1st times 5
2nd times -2
1st times 4
2nd times -3
10x + 15y = 25
-10x – 8y = -32
7y = -7
y = -1
8x + 12y = 20
-15x – 12y = -48
-7x
= -28
x= 4
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
3x – 6y = 18
(-24,-15)
2) x + y = 8
x–y=4
(6,2)
Elimination with Multiplication
1) -3x – 4y = 2
-2x + y = -6
2) x – 2y = -1
-2x + 4y = 2
Answers:
1. (2,-2)
2. Infinitely
Many
Elimination with Multiplication
1) 4x + 3y = 19
3x – 4y = 8
2) 4x – 7y = 10
3x + 2y = -7
Answer: (4,1)
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