Inequalities With Linear Systems

Vocabulary

1. Linear2. Inequality3. Variable4. Greater Than5. Less Than6. Equal To7. Substitution

Method8. Number Line

9. Symbol10. Solution11. Equation12. Fraction13. Decimal14. Point of

Intersection15. Linear System16. Combination

Method17. Geometry18. Algebra19. Problem

Solving Strategies

20. Midpoint

Symbols

Greater Than > Less Than <Equal To =

Greater Than or Equal To >Less Than or Equal To <

Number Lines

Using a Number Line3X + 4 < 13

0What numbers satisfy this equation?

3X + 4 < 13-What numbers satisfy this equation?

Number Line Solving

1. 3x + 12 = 5x -42. 3w + 12 < 5w -43. q- 5 = 6q + 104. r – 5 > 6r + 105. 3x + 17 < 476. -6x +9 < 257. 18 < -4X +28. 43 < 8X -99. 14x -23 < 5x + 13

10. 3,975 + 6d < 995 + 17.95d

Point of Intersection

Point of Intersection

0Where two lines meet/touch/cross0Found using the 6 Step Method0Found using the Substitution Method0Found using the Combination Method

Problem Solving Strategies

1. Make A Table2. Draw a Picture3. Solve a Simpler Problem4. Make an Equation5. Work Backwards6. Guess and Check

6 Step Method

1. Set Equations Equal2. Get All X’s on One Side3. Get All Numbers on One Side4. X = ?5. Substitute X Back Into One Equation6. Point of Intersection

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?

2.1 Continued

1. For what number of days will the costs for the two companies be the same? What is that cost?

2. For what numbers of days will Super Locks cost less than Fail Safe?

3. For what numbers of days will Super Locks cost less than $6000?

4. What is the cost of one year of service from Fail Safe?5. How can Fail Safe adjust its per-day charge to make

its cost for 500 days of service cheaper than Super Locks’ cost?

2.1 Continued

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

Problem 2.2

C = 3,975 + 6d (Super Locks)

C= 995 + 17.95d (Fail Safe)

Find Point of Intersection:1. Using 6 Step Substitution Method2. Using Combination Method

Applications Pg. 300 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. a. Write an equation relating the rental cost for each company

to the miles driven.b. Graph the equationsc. Under what circumstances is the rental cost the same for

both companies? What is that cost?d. Under what circumstances is renting from Zippy cheaper

than renting from A+?e. Suppose Sam rents a car from A+ and drives it 225 miles.

What is his rental cost?

Applications Pg. 30

0 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.a. Write equations that show Maggie and Ming’s distances

from school t minutes after they leave their homesb. When, if ever will Maggie catch up with Ming?c. How long will Maggie remain behind Ming?d. At what times is the distance between the two girls less

than 50 meters?

Substitution Method

1. Get both variables on separate sides2. Get either x or y completely by itself3. Substitute into the other equation4. Solve5. Substitute again to find the second variable value

Substitution Problems

0Page 56 A. 1-6

Combination Method

1. Get X and Y on the Same Side2. Make Sum of 2 Equations = Sum of Totals3. Solve for X4. Plug X Back Into an Equation From Step One5. Solve for Y

Combination Problems

0Page 58 A. 1-3

Solve Using Any Method

Graphing

Pg. 40

0Write each equation in y=mx + b form.1. x – y = 42. 2x + y = 93. 8x + 4y = -124. 12 = 3x -6y5. x + y =2.56. 600 = 5x + 10y

Parallel and Perpendicular Lines Pg. 46

0Write an equation of a line parallel to the given line.36. y= 4x + 637. -6x + y = 338. x + y = 939. x + 4y = -2040. Y = -(3/4)x -241. 7x + y = -12Write an equation of a line

perpendicular to the given line42. y = -4x +243. y = -(2/3)x -744. y = 6x +1245. -2x + y = -146. x – 4y = 2047. 2x + 3y = 8

0Without graphing, decide whether the lines are parallel, perpendicular, or neither.a. 3x + 6y =12 and y = 10 + -(1/2)xb. Y = -x +5 and y = x +5c. Y = 2 – 5x and y = -5x +2d. Y = -3 +5x and y = -(x/5) +3e. 10x +5y = 20 and y = 10x + 20

Parallel and Perpendicular Lines Pg. 48

0Suppose 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?

Parallel and Perpendicular Lines Pg. 47

Coordinates

0Tell whether each ordered pair is a solution of 3x – 5y = 15.a. (-2, -4)b. (0, -3)c. (-10, 9)d. (-5, -6)e. (-10, -9)f. (-4, -5.4)Which equation is

equivalent to 3x + 5y = 15?

g. 3x = 5y +15h. x = -5y +5i. y = 0.6 x +3j. y = -0.6x + 3

Problem Solving With Graphs

1. Graph both equations2. Estimate a Point of Intersection 3. Check Your Table to See if You Were Right4. Determine the Inequality Conditions5. Shade the Appropriate Area6. Label your Graph and Conclude

Problem Solving With Graphs

Investigation 5 Page 69 -81