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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 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). Solution: (-3, -3) 2x + 3 = -x - 6 3x + 3 = -6 3x = -9 x = -3 Check: 2(-3) + 3 = -(-3) - 6 -6 + 3 = 3 - 6 -3 = -3

Graph: y = 2x - 2 Graph: y = 2(x + 1) + 1 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). Solution: No Solution 2x - 2 = 2(x + 1) + 1 2x - 2 = 2x + 2 + 1 2x - 2 = 2x + 3 No Solution Since the ROC’s are the same and the y-intercepts are different the lines are parallel resulting in No Solution.

Graph: y = ½x - 3 Graph: y = ½(x - 4) - 1 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). Solution: Infinitely Many Solutions ½x - 3 = ½(x - 4) - 1 ½x - 3 = ½x - 2 - 1 ½x - 3 = ½x - 3 Infinitely Many Solutions Since the ROC’s are the same and the y-intercepts are the same the lines have Infinitely Many Solutions Check: ½(2) - 3 = ½(2 - 4) - 1 -2 = -2 (2, -2)

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

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

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