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)
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)