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Algebra 1
Lesson 8.3
Linear Combination
Whadda ya know 'bout...

What things cancel
each other out?
Real-life example:
What is the volume of this apple in fluid ounces?
Real-life example:
Do the following systems meet the criteria?

2x + 5y = -6

9x - 2y = 12

2x + 3y = 14

3x + 6y = 4

6x + y = 2

x + y = 16

3x - y = 7

2x + 2y = 8

x + y = -8

5x - 8x = 22

x - y = 10

5x + 8x = -19
Linear Combination- My turn:

x - 3y = -1
2x + 3y = 16

add/sub.
Goal: eliminate a variable!
through addition or subtraction

Turn a variable
into ZERO
What is linear combination?

linear

solving a system of linear equations by
eliminating a variable by adding or
subtracting the equations.
aka addition-and-subtraction method
aka elimination method
Do the following systems meet the criteria?

2x + 5y = -6

9x - 2y = 12

2x + 3y = 14

3x + 6y = 4

6x + y = 2

x + y = 16

3x - y = 7

2x + 2y = 8

x + y = -8

5x - 8x = 22

x - y = 10

5x + 8x = -19
Do the following systems meet the criteria?

2x + 5y = -6

9x - 2y = 12

2x + 3y = 14

3x + 6y = 4

6x + y = 2

x + y = 16

3x - y = 7

2x + 2y = 8

x + y = -8

5x - 8x = 22

x - y = 10

5x + 8x = -19
Our turn:

x+y=9
x - 3y = 5

add/sub.
Your turn:

10x - 2y = 24
6x + 2y = 8

Your
add/sub.
Your turn:

2x + 3y = 13
5x + 3y = 1

Your
add/sub.
http://www.youtube.com/watch?v=1qHTmxlaZWQ

All I Do Is Solve- Math Rap
linear combination WITH multiplication
Alg1 8.3 Linear Combination

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Alg1 8.3 Linear Combination