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2. ANSWER: inconsistent Chapter 6 Use the graph below to determine whether each system is consistent or inconsistent and if it is independent or dependent. 3. DANCES Mario and Tanesha are inflating balloons for the school dance. Mario has 12 balloons inflated and is inflating additional balloons at a rate of 3 balloons per minute. Tanesha has 16 balloons inflated and is inflating additional balloons at a rate of 2 balloons per minute. a. Write a system of equations to represent the situation. b. Graph each equation. c. How long will it take Mario to have more balloons filled than Tanesha? 1. ANSWER: a. Mario: ANSWER: consistent and independent , Tanesha: 2. ANSWER: inconsistent 3. DANCES Mario and Tanesha are inflating balloons for the school dance. Mario has 12 balloons inflated and is inflating additional balloons at a rate of 3 balloons per minute. Tanesha has 16 balloons inflated and is inflating additional balloons at a rate of 2 balloons per minute. a. Write a system of equations to represent the situation. b. Graph each equation. c. How long will it take Mario to have more balloons filled than Tanesha? ANSWER: a. Mario: b. c. (4, 24); Mario will have more filled balloons after 4 minutes. Use substitution to solve each system of equations. 4. ANSWER: , Tanesha: 5. ANSWER: no solution 6. ANSWER: eSolutions Manual - Powered by Cognero b. Page 1 number is two. The sum of the two numbers is fourteen. What are the two numbers? 5. ANSWER: Chapter 6 no solution ANSWER: 4 and 10 Use elimination to solve each system of equations. 6. ANSWER: 12. ANSWER: (2, 1) 7. ANSWER: infinitely many 8. FRUIT Sarah and Toni each bought fruit for a fundraiser. If Toni spent $4.30 and Sarah spent $2.80, how much does each type of fruit cost? 13. ANSWER: 14. CARNIVALS Scott and Isaac went to the school carnival. Use the table shown to determine how many tickets a ride and game each cost. ANSWER: apple, $0.30; orange, $0.50 ANSWER: ride, 3 tickets; game, 1 ticket Use elimination to solve each system of equations. 9. ANSWER: 15. SAVINGS Caleb made $105 mowing lawns and walking dogs, charging the rates shown. If he mowed half as many lawns as dogs walked, how many lawns did he mow and how many dogs did he walk? 10. ANSWER: (0, 2) ANSWER: lawns, 3; dogs, 6 11. The difference of three times a number and a second number is two. The sum of the two numbers is fourteen. What are the two numbers? Determine the best method to solve each system of equations. Then solve the system. ANSWER: 4 and 10 Use elimination to solve each system of equations. 16. ANSWER: elim (+); (-4, 14) 12. ANSWER: (2, 1) eSolutions Manual - Powered by Cognero 17. Page 2 ANSWER: subst; (2, 5) 16. ANSWER: Chapter 6 (-4, 14) elim (+); 17. 20. ANSWER: subst; (2, 5) ANSWER: 18. BABYSITTING Kelsey and Emma babysit after school to earn extra money. Kelsey made $52 by charging $10 per hour and $4 per child. Emma made $67.50 by charging $15 per hour and $2.50 per child. a. Write a system of equations to represent the situation. b. How many hours and how many children did each babysit? ANSWER: a. b. 4 hours, 3 children Solve each system of inequalities by graphing. 19. ANSWER: 20. ANSWER: eSolutions Manual - Powered by Cognero Page 3