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 - 2

Graph: y = -x - 6

Solution 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 - 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 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 Solution

2x - 2 = 2(x + 1) + 12x - 2 = 2x + 2 + 12x - 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 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

½x - 3 = ½(x - 4) - 1½x - 3 = ½x - 2 - 1½x - 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 + 594x + 7 = 59

4x = 52x = 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 + 13x + 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 = -

13Solution: (-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 + 13/2½x + 3/2 + 5 = ½x + 13/2½x + 13/2 = ½x +

13/2Infinitely Many Solutions

Check: ½ (-3 + 3) + 5 = ½(-3) + 13/2 ½(0) + 5 = ½(-3) +

13/20 + 5 = -3/2 + 13/25 = 5

Solution: (-3, 5)

Note: This is one of many solutions