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