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6 DATE PERIOD Chapter 6 Test, Form 3 Graph each system of equations. Determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it. 1 1. − y=x 3 y+x+4=0 SCORE 1. 1 y=x 3 3x - 4y = 8 x O 2. x + 3y = 3 y+x+4=0 3y = -x + 9 Use substitution to solve each system of equations. If the system does not have exactly one solution, state whether it has no solution or infinitely many solutions. 3. y = 2x - 7 y one solution; (-1, -3) AM-60C-827731-A y 3y = -x + 9 4. 4y - 3x = 5 x 3 − x=y-4 O 4 x + 3y = 3 5. x - 2y = -3 y = 3x - 1 6. y = -x + 3 x + y = -1 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Use elimination to solve each system of equations. 7. 6x - 7y = 21 3x + 7y = 6 2 y = -8 9. 2x + − 3 1 1 − x-− y=1 2 3 8. 0.2x + 0.5y = 0.7 -0.2x - 0.6y = -1.4 1 2 10. − x+− y = -10 2 5 25x + 10y = 2415 1 - 2x 12. 7y = 2− 2 5x = 3y - 4 13. Three times one number added to five times a second number is 68. Three times the second number minus four times the first number is 6. What are the two numbers? 14. The difference of two numbers is 5. Five times the lesser number minus the greater number is 9. What are the two numbers? 15. A trail mix that costs $2.45 per pound is mixed with a trail mix that costs $2.30 per pound. How much of each type of trail mix must be used to have 30 pounds of a trail mix that costs $2.35 per pound? Chapter 6 5. (1, 2) 6. no solution 7. (3, - −37 ) 3x + 6y = -6 Determine the best method to solve each system of equations. Then solve the system. 11. x + y = 147 no solution AM-61C-827731-A (4, 1) 3. no solution 4. 2. 61 8. (-14, 7) 9. (-2, -6) (-32, 15) 10. 11. substitution; (63, 84) elimination (×); 12. 13. 14. (- −12 , −12 ) 6, 10 1 1 3− , 8− 2 2 10 lb of $2.45 mix; 15. 20 lb of $2.30 mix Glencoe Algebra 1 Assessment NAME NAME DATE 6 Chapter 6 Test, Form 3 PERIOD (continued) 16. A boat travels 60 miles downstream in the same time it takes to go 36 miles upstream. The speed of the boat in still water is 15 mph greater than the speed of the current. Find the speed of the current. 16. 5 mph For Questions 17 and 18, solve the system of inequalities by graphing. 1 x+2 17. y < - − 17. 4 y y≤x-1 O 18. -2x - y > 1 18. 1 − x-y≤1 x y C06-12A-890500-A 2 O x Bonus Find the area of the polygon formed by the system of equations y = 0, y = 2x + 4 and -3y - 4x = -12. Chapter 6 62 B: 10 square units Glencoe Algebra 1 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 19. Mr. Nordmann gets a commission of $2.50 on each pair of women’s shoes he sells, and a commission of $3 on each pair C06-13A-890500-A of men’s shoes he sells. To meet his sales targets, he must sell x = women’s shoes at least 10 pairs of women’s shoes and at least 5 pairs of sold; y = men’s shoes men’s shoes. He also wants to make at least $60 a week in sold; x ≥ 10, y ≥ 5, commissions. Define the variables, write a system of 2.5x + 3y ≥ 60; sample inequalities to represent this situation, and name one possible answer: (15, 10) solution. 19.