1 Algebra I Chapter 6 Test Review Standards/Goals: D.1.g: I can solve systems of equations in a variety of methods, including: graphing, substitution and elimination. A.REI.12.: I can graph the solution of a linear inequality in a half-plane. A.REI.12: I can graph a system of linear inequalities. A.CED.2.: I can create at least two equations in two or more variables to represent relationships between quantities. #1. Concept Question: Suppose that a system of equations has been graphed and in the process of graphing the two equations, it is determined that the slopes of the two lines are the same. It is also determined that the y-intercepts are different. How many solutions will this system have? #2. Concept Question: Consider the system of equations below. If you were instructed to use elimination to solve it, what would be your first step? 123x + 68y = 1203 93x + 68y = 948 #3. Concept Question: Consider the following system of inequalities: x 0 y 0 If you were to graph these inequalities, what quadrant would show the correct set of solutions to the system of inequalities? #4. Reading Comprehension: Read the following passage: You have to go to Wal-Mart to buy some new supplies for school. You need to get two types of notebooks: large & small. Some of your classes require large notebooks and other classes require the smaller ones. Suppose you want to buy 6 notebooks. The store sells small notebooks for $8 and large notebooks for $10. If you buy 6 notebooks and spend $56, how many of each size notebook did you buy? If you can write two equations, using x to represent the small notebooks and y to represent the larger notebooks, the system would look like the following: x + y = 6 You are to buy a total of 6 notebooks. 8x + 10y = 56 x small notebooks for $8 plus y large notebooks for $10 adds up to $56. If you solve this system, you find that you will need to buy 2 small notebooks. READING QUESTIONS: a. In the situation described above, what does x represent? b. In the situation described above, what is the value of y?
2 #5. Cookies: Cookies worth $3.25 a pound were mixed with cookies worth $4.79 a pound to produce a mixture worth $3.79 a pound. How much of each kind of cookie was used to produce 25 pounds of the mixture? Define a two variables, set up a system of equations and solve. #6. Planes: A plane has 15 passengers. Some have 1 bag and others have 2 bags. There are a total of 33 bags. Let b = the number of passengers with 1 bag and t = the number of passengers with 2 bags. Write a system describes this situation. DO NOT SOLVE #7. Store: At a cd and dvd bookstore, cd s sell for $10 each and dvd s sell for $15 each. You purchase 40 items and spend $450. How many cd s did you buy? Define variables and write a system describes this situation.do NOT SOLVE #8. Fruit: A fruit market is selling oranges in a 5 lb bag for $6 and a 10 lb bag for $10. You spend $68 and buy a total of 8 bags of oranges. Using a system of equations, how many 5 lb bags and 10 lb bags of oranges did you buy? Define variables and write a system describes this situation. How many total pounds of oranges did you buy?
3 #9. Tests: A student took 60 minutes to answer a combination of 20 multiple choice and extended response questions. She took 2 minutes to answer each multiple choice question and 6 minutes to answer each extended response question. Write a system of equations to model this relationship between the number of multiple choice questions 'm' and the number of extended response questions 'r'. DO NOT SOLVE. #10. Coins: Suppose you have 12 coins that total 32 cents. Some of the coins are nickels and the rest are pennies. How many of each coin do you have? #11. Sandwiches: Two groups of people order food at a restaurant. One group orders 4 hamburgers and 7 chicken sandwiches for $34.50. The other group orders 8 hamburgers and 3 chicken sandwiches for $30.50. Find the cost of each item. Write a system describes this situation. DO NOT SOLVE #12. Dance Hall: Tickets for a dance are sold for $5 to seniors and $7 to juniors. The dance hall can hold at most 560 students. How many of each type of ticket must be sold to raise at least $3,500? Write a system of inequalities to describe this situation. Be sure to define your variables. #13. Entertainment: Hideo plans to spend no more than $60 at an entertainment store on DVDs and CDs. DVDs cost $17 each and CDs cost $14 each. He wants to buy at least two items. Write a system of linear inequalities that describes the situation. Write a system of inequalities to describe this situation. Be sure to define your variables.
4 #14. Inequalities: Consider the system of inequalities that have been graphed in the diagram below. Answer the following: a. Where is the approximate intersection point of the two lines? b. Write a few ordered pairs that would represent a possible solution to the system. c. Write a few ordered pairs that would NOT represent possible solutions to the system. #15. Inequalities: Write a system of inequalities for the following graph: a. b.
5 #16. Inequalities: Graph the following system: 2x y < 1 x + 2y < -4 FLASHBACK SECTION: Solve each inequality, graph the solution and write an interval for its solution. #1. -5x > 70 #2. -8 < 2x 6 18 #3. -2 x + 5 + 10 > 22 #4. 10 + x + 9 < 8 #5. 4 8x 9 > 20 #6. x + 7 + 18 = 17 #7. 10 + x 40 = 7
6 #8. 2 x 8 #9. 9 x 18 #10. What is the domain for the relation: y = x + 8 x 8? Which 2 quadrants in the Cartesian coordinate plane contain the line whose equation is: #11. y + 8 = 0? #12. y 9 = 0? #13. x 4 = 0? #14. x + 2 = 0? #15. Write an equation that would be in standard form and would be parallel to each of the following equations: 5x + 7y = 1-5x + 3y = 12-6x + 7y = 13-4x + 28y = 20 #16. What is the equation, in standard form, of the line that passes through (10, -6) and has a slope of ½? #17. What is the equation, in standard form, of the line that passes through (10, -6) and has a slope of 2/3?