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Sec 5.4 S olving Special Systems of Linear Equations

Learn to classify systems of linear equations as having one solution, no solution, or infinite solutions using slope and y-intercept. Practice solving systems by substitution, graphing, and elimination methods.

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Sec 5.4 S olving Special Systems of Linear Equations

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  1. Sec 5.4Solving Special Systems of Linear Equations

  2. Classifying Systems of Equations One Solution – The lines intersect No Solution – The lines are parallel Infinite Number of Solution – The graphs are the same line One Solution No Solution Infinite Solutions

  3. Using m and b to classify systems If the slopes are different, the system has one solution If the slopes are the same and the y-intercepts are different, the system has no solution If the slopes are the same and the y-intercepts are same, the system has infinite solutions

  4. Ex #1 Without graphing, determine if the system has one solution, no solution or infinitely many solutions m = 2, b = –4 a. No Solution m = 2, b = 6 m = ⅓ , b= 6 b. One Solution m = 2, b = 6 m = 2, b = 3 c. Infinitely Many Solutions m = 2, b = 3

  5. Ex #2: Solve the following system: By Substitution: By Graphing: • • False, NO SOLUTION • By Elimination: • y = 2x – 5 y = 2x + 1 • • Lines parallel, NO SOLUTION False, NO SOLUTION

  6. Ex #2: Solve the following system: By Substitution: By Graphing: • • True, INFINITE SOLUTIONS • By Elimination: –2x + y = 3 –4x + 2y = 6 Same line, INFINITE SOLUTIONS True, INFINITE SOLUTIONS

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