1 / 14

Mastering Linear Systems: Substitution, Elimination & Graphing

Learn the main ways of solving linear systems in algebra II: substitution, elimination, and graphing. Step-by-step examples and methods with practice exercises included.

fuhr
Download Presentation

Mastering Linear Systems: Substitution, Elimination & Graphing

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Do Now

  2. 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

More Related