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7.4 Consistent and Inconsistent Systems

7.4 Consistent and Inconsistent Systems. Objectives: Identify consistent and inconsistent systems of equations. Identify dependent and independent systems of equations .

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7.4 Consistent and Inconsistent Systems

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  1. 7.4 Consistent and Inconsistent Systems Objectives: Identify consistent and inconsistent systems of equations. Identify dependent and independent systems of equations. Standards addressed: 2.8.8.H: Graph a linear function. 2.8.11.F: Identify whether systems of equations are consistent or inconsistent.

  2. A system of equations may have one unique solution, infinitely many solutions, or no solution at all. • Systems that have one or infinitely many solutions are called consistent. • Systems with no solutions are called inconsistent.

  3. Ex. 1

  4. Ex. 2b. Determine whether the system is consistent or inconsistent by solving it algebraically and graphically. • Multiply 1st EQ by -2 -2x – 6y = -2 2x + 6y = 3 0 = 5 Inconsistent No solution

  5. Ex. 3a.

  6. Ex. 3b • Multiply 2nd EQ by -2 • 4y = -2x – 6 -4y = 2x + 6 0 = 0 Dependent infinity

  7. Ex. 4

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