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Special Types of Linear Systems

Special Types of Linear Systems. Math Tech II Everette Keller. What is a Linear System?. Two of more linear equations in the same variable form a system of linear equations , or simply a linear system . . What is a Type of Systems Have We Dealt With ?. Intersecting.

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Special Types of Linear Systems

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  1. Special Types of Linear Systems Math Tech II Everette Keller

  2. What is a Linear System? Two of more linear equations in the same variable form a system of linear equations, or simply a linear system.

  3. What is a Type of Systems Have We Dealt With? Intersecting

  4. Example of an Intersecting System y = 3x y = x + 4

  5. What Other Types Of Systems Are There? Parallel Coinciding

  6. Activity Time

  7. Example of a Parallel System -x + y = 7 -x + y = 0

  8. Example of a Parallel System Solve using a method other than graphing -x + y = 7 -x + y = 0 0 ≠ 7 Thus there is no solution

  9. Example of a Coinciding System 2x + y = 2 4x + 2y = 4

  10. Example of a Coinciding System Solve using a method other than graphing 2x + y = 2 4x + 2y = 4 4 = 4 Thus there are infinitely many solution

  11. Summary of Special Types Of Linear Systems 1 – If the two equations have different slopes, then the system has one solution and the lines intersect 2 – If the two equations have the same slope but different y – intercepts, then the system has no solution and the lines are parallel 3 – If the two equations have the same slope and the same y – intercept, then the system has infinitely many solutions and the lines coincide

  12. Example Find the solution to the linear system by any method -2x + 4y = 1 3x – 6y = 9

  13. Example Find the solution to the linear system by any method 2x + y = 4 -4x – 2y = -8

  14. White Board Example Find the solution to the linear system by any method 2x – 2y = 4 -x + y = -2

  15. White Board Example Find the solution to the linear system by any method -x + y = 1 x – y = 1

  16. White Board Example Find the solution to the linear system by any method 5x + 3y = 17 x – 3y = -2

  17. Closing Minutes • What are the different types of systems that can occur? • What does it mean for a system to have no solution? • What does it mean for a system to have infinitely many solutions? • What does it mean for the lines to linear functions in a system to intersect?

  18. Closing Minutes What are some contextual situation that these types of systems occur?

  19. Homework Find a real life problems that relate to the various types of systems and state it for the next class period Problems 1 – 10 on the Handout

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