Unit 5 Test Review Systems of Linear Equations Name Class Date
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1 Unit 5 Test Review Systems of Linear Equations Name Class Date Find the mistake - The following problems have been solved HOWEVER there could be a mistake. Each question is worth 3 points: 1pt the mistake, 1pt-explain what the mistake is, 1pt solve the problem correctly 1. Solve the equation using graphing The solution Is (2,3) 2. How many solutions does the following system have Same slope and same y intercept means they will be the same line which have no solutions. 3. Solve the following system Solution Multiple Choice 4. If you try to solve a linear system by the substitution method and get the result 8 = 8, what does this mean? a. The system has one solution (8,8) b. The system has one solution (-8,-8) c. The system has no solution d. The system has an infinite number of solutions 5. Matt solved the system by substituting for y in Which is the value of x in the solution of the system? a. -4 b. -2 c. 2 d. 4
2 6. The cost for an eighth grade party is $375 for room rental, entertainment, and decorations, plus $17 per person for food. Tickets for the party are sold for $20. What is the break-even point? a. 100 tickets b. 125 tickets c. 150 tickets d. 200 tickets 7. How many solutions does the system have? a. 0 b. 1 c. 2 d. Infinite solution 8. A DJ charges $75 for set up and transportation, plus $20 per hour to entertain at a party. Which equation represents the relationship between the cost, y (in dollars, and the number of hours, x, for which the DJ is hired? a. b. c. d. 9. Solve the following system a. (6,3) b. (3,6) c. No Solution d. Infinite Solutions Free Response 10. You are planning to rent a canoe. You find two stores that rent canoes and want to find the best price. Henry s Hut charges a rental fee of $20 plus $3 for each hour you have the canoe. Outdoor Olivers charges a flat rate of $50. a. Write an equation for Henry s Hut. b. Write an equation for Outdoor Olivers. c. Find the time when renting from either places would be the same price. d. If you plan to rent a canoe for 6 hours who should you rent from? Justify your answer. 11. Determine if there is one solution, no solution, or an infinite number of solutions. Justify your answer. 12. Consider the linear system shown a. Describe the first step you would take to solve the system using the substitution method and identify the variable that will be solved for when you combine the equation b. Solve the system
3 13. Nicholas is shopping for 13 gifts. He can buy 7 audio books and 6 DVDs for $119, or he can buy 10 audio books and 3 DVDs for $92. a. Write a system of equations to represent the situation. Let x represent the price of an audio book and y represent the price of a DVD b. Solve the system using the linear combination (elimination). c. Interpret your solution in the context of the problem. 14. Justin wants to join a health club. He is considering Let s Get Moving, which charges a one-time initiation fee of $192 plus a $18 monthly membership fee. He is also considering Fitness for Life, which charges $42 per month with no initiation fee. a. Write an equation that gives the total cost of Let s Get Moving in terms of the number of months of membership. b. Write an equation that gives the total cost of Fitness for Life in terms of the number of months of membership. c. Calculate the total cost of membership in each club for 5 months. Which club is a better deal for 5 months of membership? d. Calculate the total cost of membership in each club for 11 months. Which club is better deal for 11 months of membership? e. Calculate the total cost of membership in each club for 16 months. Which club is a better deal for 16 months of membership? f. Write a system of equations for the problem situation. g. When is the cost of belonging to both clubs the same? What is this cost?
4 15. Solve each linear system using the specified method. a. c. b. Review 16. Solve the following equation 17. How many solutions does the following equation have 18. Graph the following equations a. b. c. 19. Given the piece of information fill in the rest of the table Equation: Table: x( ) y( ) Story: Rachel received her first cell phone bill. She is charged a service fee of $35 and an additional $0.75 for each text she sends. Graph
5
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