1. Do Now

2. Solving Linear Systems
Algebra II
Solving Linear Systems

3. We will focus on 1 and 2 today.
Main ways of solving
Substitution
Elimination
Graphing
We will focus on 1 and 2 today.

4. First Method: Substitution
1) Pick an equation and isolate a variable. 2) Plug value from step 1 into the second equation. Solve. 3) Plug value of the variable from step 2 into any equation. Solve. 4) Final answers is a coordinate: (x, y)

5. Substitution Example
1.) x + 2y = 6 3x – 2y = 2

6. Substitution Examples
2.) 4x + y = 7 3.) x + 3y = 3 2x + 5y = -1 2x – 4y = 6

7. Substitution Examples
4.) 2x – 3y = 3 5.) 2x – 5y = 9 -2x + y = -4 -3x + y = -7

8. Second Method: Elimination
1) Change equation(s) so that you have
opposite coefficients for one of the variables.
2) Add equations straight down. Solve.
3) Take value of the variable from step 2 and plug into any equation. Solve.
4) Final answer is the coordinate (x, y).

9. Solve the system using elimination
1.) x – y = 7
2x + y = 5

10. Solve the system using elimination
2.) x + 2y = -11
3x – 2y = -1

11. Solve the system using elimination
3.) 3x – y = 4
2x + 3y = 32

12. Solve the system using elimination
4.) 2x + 5y = 0 4x + 6y = 24

13. Solve the system using elimination
5.) 3x – 4y = -4 -5x + 2y = 2

14. Homework
Systems of Linear Equations Worksheet
# 5-8, 15-18