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Topics: Topic 1: Solving Linear Equations Topic 2: Solving Quadratic Equations

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.

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Topics: Topic 1: Solving Linear Equations Topic 2: Solving Quadratic Equations

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  1. 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

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

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

  4. Graph: y = ½x - 3 Graph: y = ½(x - 4) - 1 Solution: Infinitely Many Solutions ½x - 3 = ½(x - 4) - 1 ½x - 3 = ½x - 2 - 1 ½x - 3 = ½x - 3 Infinitely Many Solutions Solution of a System The place where two (or more) graphs intersect is the solution of the system. The solution is written as an ordered pair (x, y). Check: ½(2) - 3 = ½(2 - 4) - 1 -2 = -2 (2, -2) Since the ROC’s are the same and the y-intercepts are the same the lines have Infinitely Many Solutions

  5. Graph: y = 6x + 7 Graph: y = 3(x + 5) - 7 Graph: y = 2x + 59 Graph: y = 2x + 1 6x + 7 = 2x + 59 3(x + 5) - 7 = 2x + 1 3x + 15 - 7 = 2x + 1 4x + 7 = 59 3x + 8 = 2x + 1 4x = 52 x + 8 = 1 x = 13 x = -7 Check: 3(-7 + 5) - 7 = 2(-7) + 1 Check:6(13) + 7 = 2(13) + 59 3(-2) - 7 = 2(-7) + 1 78 + 7 = 26 + 59 -6 - 7 = -14 + 1 85 = 85 -13 = -13 Solution: (13, 85) Solution: (-7, -13)

  6. Graph: y = -6x + 17 Graph: y = ½(x + 3) + 5 Graph: y = -3x + 25 Graph: y = ½x + 13/2 -6x + 17 = -3x + 25 ½(x + 3) + 5 = ½x + 13/2 ½x + 3/2 + 5 = ½x + 13/2 -3x + 17 = 25 ½x + 13/2 = ½x + 13/2 -3x = 8 Infinitely Many Solutions x = -8/3 Check: ½ (-3 + 3) + 5 = ½(-3) + 13/2 Check: -6(-8/3) + 17 = -3(-8/3) + 25 ½(0) + 5 = ½(-3) + 13/2 16 + 17 = 8 + 25 0 + 5 = -3/2 + 13/2 33 = 33 5 = 5 Solution: (-8/3, 33) Solution: (-3, 5) Note: This is one of many solutions

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