topics: topic 1: solving linear equations topic 2: solving quadratic equations

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Topics: Topic 1: Solving Linear Equations Topic 2: Solving Quadratic Equations Topic 3: Solving Proportions involving linear and quadratic functions. Topic 4: Solving Absolute Value Equations. Graph: y = 5x - 2. Graph: y = -x - 6. Solution: (-3, -3). 2x + 3 = -x - 6. 3x + 3 = -6. - PowerPoint PPT Presentation

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  • Topics:Topic 1: Solving Linear EquationsTopic 2: Solving Quadratic EquationsTopic 3: Solving Proportions involving linear and quadratic functions.Topic 4: Solving Absolute Value Equations

  • Graph: y = 5x - 2Graph: y = -x - 6Solution of a SystemThe place where two (or more) graphs intersect is the solution of the system. The solution is written as an ordered pair (x, y).Solution: (-3, -3)2x + 3 = -x - 63x + 3 = -63x = -9x = -3Check: 2(-3) + 3 = -(-3) - 6-6 + 3 = 3 - 6-3 = -3

  • Graph: y = 2x - 2Graph: y = 2(x + 1) + 1Solution of a SystemThe place where two (or more) graphs intersect is the solution of the system. The solution is written as an ordered pair (x, y).Solution: No Solution2x - 2 = 2(x + 1) + 12x - 2 = 2x + 2 + 12x - 2 = 2x + 3No SolutionSince the ROCs are the same and the y-intercepts are different the lines are parallel resulting in No Solution.

  • Graph: y = x - 3 Graph: y = (x - 4) - 1Solution of a SystemThe place where two (or more) graphs intersect is the solution of the system. The solution is written as an ordered pair (x, y).Solution: Infinitely Many Solutions x - 3 = (x - 4) - 1x - 3 = x - 2 - 1x - 3 = x - 3Infinitely Many SolutionsSince the ROCs are the same and the y-intercepts are the same the lines have Infinitely Many SolutionsCheck: (2) - 3 = (2 - 4) - 1 -2 = -2(2, -2)

  • Graph: y = 6x + 7 Graph: y = 2x + 596x + 7 = 2x + 594x + 7 = 594x = 52x = 13Check:6(13) + 7 = 2(13) + 5978 + 7 = 26 + 5985 = 85Solution: (13, 85) Graph: y = 3(x + 5) - 7 Graph: y = 2x + 13(x + 5) - 7 = 2x + 13x + 15 - 7 = 2x + 13x + 8 = 2x + 1x + 8 = 1x = -7Check: 3(-7 + 5) - 7 = 2(-7) + 13(-2) - 7 = 2(-7) + 1-6 - 7 = -14 + 1-13 = -13Solution: (-7, -13)

  • Graph: y = -6x + 17 Graph: y = -3x + 25-6x + 17 = -3x + 25-3x + 17 = 25-3x = 8x = -8/3Check: -6(-8/3) + 17 = -3(-8/3) + 2516 + 17 = 8 + 2533 = 33Solution: (-8/3, 33) Graph: y = (x + 3) + 5 Graph: y = x + 13/2(x + 3) + 5 = x + 13/2x + 3/2 + 5 = x + 13/2x + 13/2 = x + 13/2Infinitely Many SolutionsCheck: (-3 + 3) + 5 = (-3) + 13/2(0) + 5 = (-3) + 13/20 + 5 = -3/2 + 13/25 = 5Solution: (-3, 5) Note: This is one of many solutions

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