1. Do Now

2. Solving Linear Systems
Algebra II
Solving Linear Systems

3. Main ways of solving
Substitution
Elimination
Graphing

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. 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).

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

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

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

11. Third Method: Graphing
1) Graph both lines in the same coordinate plane.
2) Your solution is the point (x, y) where the two lines intersect.
What would be the solution if the lines are parallel?
What would be the solution if the lines overlap each other?

12. Solve by graphing

13. Solve by graphing

14. Homework
Systems of Linear Equations Worksheet
# 1-2, 5-8, 15-18