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Types of Systems

Types of Systems . Inconsistent of consistent?. Example 1: 3x – y = 2 6x – 2y = 3 Example 2: x + y = -2 x -2y = 7. Inconsistent or Consistent?. Example 3: x + 2y + z = 1 -x – y + 2z = 0 y + 3z = 4 . Dependent vs. Independent.

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Types of Systems

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  1. Types of Systems

  2. Inconsistent of consistent? • Example 1: 3x – y = 2 6x – 2y = 3 • Example 2: x + y = -2 x -2y = 7

  3. Inconsistent or Consistent? Example 3: x + 2y + z = 1 -x – y + 2z = 0 y + 3z = 4

  4. Dependent vs. Independent • A system is dependent if it has infinitely many solutions. • A system is independent if it has only one solution. • An inconsistent system can NEVER be dependent or independent.

  5. Dependent or Independent? Example 4: 5x + 2y = 3 10x + 4y = 6 Example 5: x – y = 2 x + y = 4

  6. Can also determine graphically.

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