This document covers the topic of linear combination in algebra lessons. It explains that linear combination is the process of solving a system of linear equations by eliminating a variable through addition or subtraction of the equations. It provides examples of solving systems of linear equations using this elimination or addition-and-subtraction method. It also includes practice problems for students to try applying linear combination.

1. Algebra 1
Lesson 8.3
Linear Combination

2. Whadda ya know 'bout...
What things cancel
each other out?

4. Real-life example:
What is the volume of this apple in fluid ounces?

5. Real-life example:

6. 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

7. Linear Combination- My turn:
x - 3y = -1
2x + 3y = 16
add/sub.

8. Goal: eliminate a variable!
through addition or subtraction
Turn a variable
into ZERO

9. 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

11. 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

12. 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

13. Our turn:
x+y=9
x - 3y = 5
add/sub.

14. Your turn:
10x - 2y = 24
6x + 2y = 8
Your
add/sub.

15. Your turn:
2x + 3y = 13
5x + 3y = 1
Your
add/sub.

16. http://www.youtube.com/watch?v=1qHTmxlaZWQ
All I Do Is Solve- Math Rap

19. linear combination WITH multiplication