1. Inequalities With Linear Systems

2. Vocabulary Linear Combination Method Symbol Inequality Solution
Geometry
Variable
Equation
Algebra
Greater Than
Fraction
Problem Solving Strategies
Less Than
Decimal
Equal To
Point of Intersection
Midpoint
Substitution Method
Linear System
Number Line

3. Symbols
Greater Than > Less Than < Equal To = Greater Than or Equal To > Less Than or Equal To <

4. Number Lines

5. Using a Number Line What numbers satisfy this equation?
3X + 4 < 13
What numbers satisfy this equation?
-What numbers satisfy this equation?

6. Number Line Solving 3x + 12 = 5x -4 14x -23 < 5x + 13
3w + 12 < 5w -4
3, d < d
q- 5 = 6q + 10
r – 5 > 6r + 10
3x + 17 < 47
-6x +9 < 25
18 < -4X +2
43 < 8X -9

7. Point of Intersection

8. Point of Intersection Where two lines meet/touch/cross
Found using the 6 Step Method
Found using the Substitution Method
Found using the Combination Method

9. Problem Solving Strategies
Make A Table
Draw a Picture
Solve a Simpler Problem
Make an Equation
Work Backwards
Guess and Check

10. 6 Step Method Set Equations Equal Get All X’s on One Side
Get All Numbers on One Side
X = ?
Substitute X Back Into One Equation
Point of Intersection

11. Problem 2.1
1. What kinds of equations will show how the costs for the two companies are a function of the number of days? 2. What pattern do you expect to see in graphs of the equations? 3. How can you use a graph to answer the questions about which company offers the best price?

13. 2.1 Continued
For what number of days will the costs for the two companies be the same? What is that cost?
For what numbers of days will Super Locks cost less than Fail Safe?
For what numbers of days will Super Locks cost less than $6000?
What is the cost of one year of service from Fail Safe?
How can Fail Safe adjust its per-day charge to make its cost for 500 days of service cheaper than Super Locks’ cost?

14. 2.1 Continued
B. For each company, write an equation for the cost c for days d of security services.

15. Problem 2.2 C = 3,975 + 6d (Super Locks) C= 995 + 17.95d (Fail Safe)
Find Point of Intersection:
Using 6 Step Substitution Method
Using Combination Method

16. Applications Pg. 30
Sam needs to rent a car for a one-week trip in Oregon. He is considering two companies. A+ Auto Rental charges $175 plus $0.10 per mile. Zippy Auto Rental charges $220 plus $0.05 per mile.
Write an equation relating the rental cost for each company to the miles driven.
Graph the equations
Under what circumstances is the rental cost the same for both companies? What is that cost?
Under what circumstances is renting from Zippy cheaper than renting from A+?
Suppose Sam rents a car from A+ and drives it 225 miles. What is his rental cost?

17. Applications Pg. 30
Maggie lives 1,250 meters from school. Ming lives 800 meters from school. Both girls leave for school at the same time. Maggie walks at an average speed of 70 meters per minute, while Ming walks at an average speed of 40 meters per minute. Maggie’s route takes her past Ming’s house.
Write equations that show Maggie and Ming’s distances from school t minutes after they leave their homes
When, if ever will Maggie catch up with Ming?
How long will Maggie remain behind Ming?
At what times is the distance between the two girls less than 50 meters?

18. Substitution Method Get both variables on separate sides
Get either x or y completely by itself
Substitute into the other equation
Solve
Substitute again to find the second variable value

19. Substitution Problems
Page 56 A. 1-6

20. Combination Method Get X and Y on the Same Side
Make Sum of 2 Equations = Sum of Totals
Solve for X
Plug X Back Into an Equation From Step One
Solve for Y

21. Combination Problems
Page 58 A. 1-3

22. Solve Using Any Method

23. Graphing

24. Pg. 40 Write each equation in y=mx + b form. x – y = 4 2x + y = 9

25. Parallel and Perpendicular Lines Pg. 46
Write an equation of a line parallel to the given line.
Write an equation of a line perpendicular to the given line
42. y = -4x +2
36. y= 4x + 6
43. y = -(2/3)x -7
37. -6x + y = 3
44. y = 6x +12
38. x + y = 9
45. -2x + y = -1
39. x + 4y = -20
46. x – 4y = 20
40. Y = -(3/4)x -2
47. 2x + 3y = 8
41. 7x + y = -12

26. Parallel and Perpendicular Lines Pg. 48
Without graphing, decide whether the lines are parallel, perpendicular, or neither.
3x + 6y =12 and y = (1/2)x
Y = -x +5 and y = x +5
Y = 2 – 5x and y = -5x +2
Y = -3 +5x and y = -(x/5) +3
10x +5y = 20 and y = 10x + 20

27. Parallel and Perpendicular Lines Pg. 47
Suppose you are given the line equation ax + by = c.
a. What is the slope of every line parallel to this line?
b. What is the slope of every line perpendicular to this line?

28. Coordinates
Tell whether each ordered pair is a solution of 3x – 5y = 15.
Which equation is equivalent to 3x + 5y = 15?
(-2, -4)
3x = 5y +15
(0, -3)
x = -5y +5
(-10, 9)
y = 0.6 x +3
(-5, -6)
y = -0.6x + 3
(-10, -9)
(-4, -5.4)

29. Problem Solving With Graphs
Graph both equations
Estimate a Point of Intersection
Check Your Table to See if You Were Right
Determine the Inequality Conditions
Shade the Appropriate Area
Label your Graph and Conclude

30. Problem Solving With Graphs
Investigation 5 Page