Class: Date: Math 10 - Unit 8 REVIEW WORKSHEET - Systems of Linear Equations Multiple Choice Identify the choice that best answers the question. 1. Without graphing, determine the equation whose graph intersects the graph of 7x + 7y = 10 exactly once. i) 7x + 7y = 12 ii) 28x + 28y = 40 iii) 5x + 7y = 10 a. ii b. i c. iii d. none 2. Which linear system has the solution x = 2 and y = 2? a. x + 2y = 2 2x + 4y = 4 c. x + 4y = 6 2x + 2y = 0 b. x + 3y = 5 2x + y = 1 d. 2x + y = 2 x + y = 6 3. For what value of k does the linear system below have infinite solutions? 5 6 x + y = 12 kx + 2y = 24 5 a. 24 b. 0 c. d. 6 4. Determine the number of solutions of the linear system: 4x + 5y = 102 24x 30y = 612 a. no solution c. one solution b. infinite solutions d. 2 solutions 5 3 5. Two lines in a linear system have a different slope, but the same y-intercepts. How many solutions does the linear system have? a. two solutions c. infinite solutions b. no solution d. one solution 6. Without graphing, determine the slope of the graph of the equation: 7x + 4y = 11 7 a. b. 7 c. 7 d. 4 4 4 1
7. Use the table of values to determine the solution of this linear system: x = y + 2 4x + 5y = 10 a. (0, 2) c. (0, 0) b. ( 2, 2) d. ( 2, 0) 8. Use the graph to solve the linear system: y = 5x 4 y + 4 = 3x a. (2, 4) c. (0, 4) b. (0, 2) d. (2, 2) 9. Create a linear system to model this situation: In a board game, Judy scored 5 points more than twice the number of points Ann scored. There was a total of 35 points scored. a. j 5 = 2a j + 2a = 35 b. j = 5 + 2a j + a = 35 c. j + 5 = 2a j + a = 35 d. a = 5 + 2j j + a = 35 2
10. The solution of this linear system is ( 5, y). Determine the value of y. x 4 5 y = 81 5 5 6 x y = 109 6 a. 34 b. 24 c. 14 d. 44 11. Which graph represents the solution of the linear system: y = 2x y + 5 = 3x a. Graph A c. Graph C b. Graph D d. Graph B 3
12. Determine the number of solutions of the linear system: 3x 5y = 43 9x + 15y = 21 a. two solutions c. no solution b. infinite solutions d. one solution 13. Without graphing, determine the equation whose graph intersects the graph of 6x + 6y = 11 exactly once. i) 6x + 6y = 13 ii) 24x + 24y = 44 iii) 4x + 6y = 11 a. ii b. i c. iii d. none 14. Which linear system has the solution x = 0 and y = 7? a. x + 2y = 0 2x + 4y = 0 c. x + 2y = 14 3x + 3y = 21 b. x + 3y = 15 2x + y = 20 d. 2x + y = 0 x + y = 14 15. For what value of k does the linear system below have infinite solutions? 6 7 x + y = 13 kx + 2y = 26 6 a. 26 b. 0 c. d. 7 16. For what value of k does the linear system below have infinite solutions? 2 3 x + y = 10 kx + 2y = 20 2 a. 20 b. 0 c. d. 3 12 7 4 3 17. Determine the number of solutions of the linear system: 14x + 7y = 315 16x 2y = 610 a. no solution c. two solutions b. one solution d. infinite solutions 4
Short Answer Please clearly show your process and box your final answer for full marks. 18. Determine the number of solutions of this linear system. 2x 3y = 5-6x +9y = -15 19. Determine the number of solutions of this linear system. 2x 3y = 5 10x - 15y = 20 20. Determine the number of solutions of this linear system. 2x 3y = 5 10x - 20y = 7 21. Create a linear system to model this situation. Then use substitution to solve the linear system to solve the problem. Kim has been saving dimes and nickels to buy a new toy. She has a total of 32 dimes and nickels, with a value of $2.50. How many of each type of coin does Kim have? 5
22. A submarine cruises underwater at 10 km/h and on the surface at 20 km/h. The submarine travels a distance of 400 km in 25 h. A linear system that models this situation is: u + s = 25 10u + 20s = 400 a) Graph the linear system above. b) Use the graph to solve the problem: i) How long did the submarine travel underwater? where u represents the time in hours cruising underwater, and s represents the time in hours cruising on the surface. ii) How long did it travel on the surface? 6
23. Use an elimination strategy to solve this linear system. 8x + 12y = 0 4x + 20y = 28 24. Use an elimination strategy to solve this linear system. 2x + 2y = 206 x y = 27 25. Create a linear system to model this situation: The perimeter of a rectangle is 237 ft. When its width is tripled, the perimeter increases by 66 ft. 7
26. Solve this linear system by graphing. 3x 3y = 15 x + y = 5 8
27. Create a linear system to model this situation: The cost of admission to the museum is $7.25 for adults and $5.25 for students. Yesterday, 139 admissions were sold, and the receipts were $815.75. 28. Use substitution to solve this linear system: x + 6 7 y = 67 3x + 6y = 81 29. Use substitution to solve this linear system: 2x + y = 103 4x + 3y = 141 9
30. Solve this linear system by graphing. y = 4 3x + y = 5 10
Math 10 - Unit 8 REVIEW WORKSHEET - Systems of Linear Equations Answer Section MULTIPLE CHOICE 1. C 2. C 3. D 4. B 5. D 6. B 7. A 8. C 9. B 10. C 11. A 12. C 13. C 14. C 15. D 16. D 17. B SHORT ANSWER 18. Infinite number of solutions 19. No solutions 20. One solution 21. Let d represent the number of dimes and n represent the number of quarters. d + n = 32 10d + 5n = 250 Kim has 18 dimes and 14 nickels. 22. a) b) (10, 15) 23. x = 3 and y = 2 1
24. x = 65 y = 38 25. 2l + 2w = 237 2l + 6w = 303 26. (0, 5) 27. Let a represent the number of adult admissions Let s represent the number of student admissions. a + s = 139 7.25a + 5.25s = 815.75 28. x = 55; y = 14 29. x = 45; y = 13 30. ( 3, 4) 2