Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Eigenvalues and eigenvectors wikipedia , lookup
Quartic function wikipedia , lookup
Cubic function wikipedia , lookup
Basis (linear algebra) wikipedia , lookup
Quadratic equation wikipedia , lookup
Bra–ket notation wikipedia , lookup
Elementary algebra wikipedia , lookup
System of polynomial equations wikipedia , lookup
History of algebra wikipedia , lookup
Signal-flow graph wikipedia , lookup
Name: ________________________ Class: ___________________ Date: __________ ID: A Math 10 - Unit 8 Final Review - Systems of Linear Equations Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Which linear system has the solution x = 9 and y = –1? a. x + 3y = 6 c. x + 2y = 9 2x + 2y = 16 2x + 4y = 18 b. x + 3y = 7 d. 2x + y = 9 2x + y = 15 x+y=6 ____ 2. Which linear system has the solution x = 2 and y = –4? a. x + 5y = 7 c. 5x + y = 6 –4x + 2y = –16 2x −4y = –17 b. 2x + 5y = 2 d. x + 5y = 2 –4x + y = 6 2x + 4y = 4 ____ 3. Which linear system has the solution x = 8 and y = 2.5? a. 2x + 3y = 23.5 c. 3x + 2y = 8 2x – 2y = 11 x – y = 23.5 b. x + 2y = 8 d. x + 3y = 24.5 2x – 4y = 16 2x – y = 10 ____ 4. Create a linear system to model this situation: The perimeter of an isosceles triangle is 42 cm. The base of the triangle is 6 cm longer than each equal side. a. s + b = 42 b. 2s + b = 42 c. 2b + s = 42 d. 2s + b = 42 b–6=s b+6=s s+6=b s+6=b ____ 5. 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 65 points scored. a. j = 5 + 2a b. j – 5 = 2a c. j + 5 = 2a d. a = 5 + 2j j + a = 65 j + 2a = 65 j + a = 65 j + a = 65 ____ 6. Create a linear system to model this situation: A woman is 3 times as old as her son. In thirteen years, she will be 2 times as old as her son will be. a. w = s + 3 c. w = 3s w + 13 = 2s w = 2s b. w = 3s d. w = 3s w + 13 = 2(s + 13) s + 13 = 2(w + 13) ____ 7. Create a linear system to model this situation: A rectangular field is 35 m longer than it is wide. The length of the fence around the perimeter of the field is 278 m. a. l + 35 = w b. l = w + 35 c. l = w + 35 d. l = w + 35 2l + 2w = 278 2l + 2w = 278 l + w = 278 lw = 278 1 Name: ________________________ ____ ID: A 8. Which graph represents the solution of the linear system: y = –2x + 2 y + 6 = 2x a. b. Graph B Graph A c. d. 2 Graph C Graph D Name: ________________________ ____ ID: A 9. Which graph represents the solution of the linear system: –3x – y = –4 3x – y = 2 a. b. Graph A Graph B c. d. 3 Graph C Graph D Name: ________________________ ID: A ____ 10. Use the graph to solve the linear system: y = –4x − 2 y + 2 = 2x a. b. (2, 0) (2, –2) c. d. (0, 0) (0, –2) ____ 11. Which linear system is represented by this graph? a) x – y = 2 5x + 7y = 17 b) x – y = 4 5x + 7y = 17 c) x – y = 6 6x + 7y = 17 d) x – y = 8 7x + 5y = 17 a. System d b. System b c. 4 System a d. System c Name: ________________________ ID: A ____ 12. Express each equation in slope-intercept form. 6 x + y = –121 12 13x + 6y = –2886 a. b. y = 222x −242 13 6 y=− x+ 13 6 y = −2x −242 y = −2x – 222 c. d. y = −2x −242 13 y=− x 6 y = −2x −242 13 y = − x −481 6 ____ 13. Use the table of values to determine the solution of this linear system: 6x + y = 3 2x + y = −5 a. b. (–9, –9) (2, –9) c. d. (–9, 2) (2, 2) c. (–8, –30) d. (–8, 30) c. (8, 10) d. (–8, –10) c. (–10, –12) d. (–12, –10) ____ 14. Use substitution to solve this linear system. 166 2 – x y= 5 5 14x + 7y = 322 a. (8, –30) b. (8, 30) ____ 15. Use substitution to solve this linear system. x = 4y – 32 5x + 12y = 160 a. (8, –10) b. (–8, 10) ____ 16. Use substitution to solve this linear system. x=2+y 9 x + 8y = –141 2 a. (–12, –12) b. (–10, –10) 5 Name: ________________________ ID: A ____ 17. Use substitution to solve this problem: Tanukah invested a total of $5600 in two bonds. He invested in one bond at an annual interest rate of 6% and in another bond at an annual interest rate of 8%. After one year, the total interest earned was $410.50. How much money did Tanukah invest in each bond? a. $3725 at 6%, $1875 at 8% b. $1875 at 6%, $3725 at 8% c. $4225 at 6%, $1375 at 8% d. $1375 at 6%, $4225 at 8% ____ 18. Use substitution to solve this problem: The perimeter of a rectangular field is 296 m. The length is 52 m longer than the width. What are the dimensions of the field? a. 80 m by 68 m b. 90 m by 58 m c. 100 m by 48 m d. 70 m by 78 m ____ 19. Use substitution to solve this problem: Wai Sen scored 85% on part A of a math test and 95% on part B of the math test. Her total mark for the test was 94. The total mark possible for the test was 104. How many marks is each part worth? a. b. Part A: 56 marks; part B: 56 marks Part A: 48 marks; part B: 48 marks ____ 20. Use substitution to solve this linear system: x – y = 17 1 4 97 x+ y=− 2 5 10 a. x = 3; y = 17 b. x = –14; y = –14 c. d. Part A: 56 marks; part B: 48 marks Part A: 48 marks; part B: 56 marks c. x = 3; y = –14 d. x = 3; y = 3 d. 35 d. 21 ____ 21. The solution of this linear system is (–6, y). Determine the value of y. 3 39 x– y=− 4 4 8 31 x–y=− 9 3 a. 15 b. 25 c. 5 ____ 22. The solution of this linear system is (–31, y). Determine the value of y. 1 1 83 x– y=− 2 4 4 6 480 x – 2y = − 7 7 a. 26 b. 31 c. 6 41 Name: ________________________ ID: A ____ 23. Use an elimination strategy to solve this linear system. 20x − 15y = 50 10x + 25y = 90 a. x = 14 and y = 2 c. x = 4 and y = 2 37 26 b. x = and y = d. x = 2 and y = 4 7 7 ____ 24. Use an elimination strategy to solve this linear system. 9x − 6y = 15 6x + 21y = 60 a. x = 3 and y = −2 c. x = 3 and y = 2 1 14 b. x = and y = d. x = −3 and y = −2 5 5 ____ 25. Use an elimination strategy to solve this linear system. 2 3 m + n = 16 3 4 1 3 − m + n = 18 2 8 a. m = −12 and n = 32 c. m = 12 and n = −32 201 52 32 b. m = and n = d. m = −12 and n = 10 15 3 ____ 26. Model this situation with a linear system: Frieda has an 11% silver alloy and a 25% silver alloy. Frieda wants to make 23 kg of an alloy that is 43% silver. c. s + t = 23 and 0.11s + 0.25t = 0.43 a. s + t = 0.43 and 0.11s + 0.25t = 23 b. s + t = 43 and 0.11s + 0.25t = 23 d. s + t = 23 and 0.11s + 0.25t = 9.89 ____ 27. Use an elimination strategy to solve this linear system. 20x − 24y = −52 8x + 32y = 104 a. x = −1 and y = −3 c. x = 1 and y = −3 b. x = 3 and y = 1 d. x = 1 and y = 3 ____ 28. Use an elimination strategy to solve this linear system. 2 1 x + y = −11 3 7 1 1 x − y = −10 7 3 a. x = −21 and y = 21 c. x = 21 and y = −21 b. x = 21 and y = 21 d. x = −21 and y = −21 ____ 29. Without graphing, determine the slope of the graph of the equation: 7x + 4y = 12 7 7 a. b. – c. 4 4 4 7 d. 7 Name: ________________________ ID: A ____ 30. Without graphing, determine which of these equations represent parallel lines. i) –7x + 7y = 10 ii) –5x + 7y = 10 iii) –3x + 7y = 10 iv) –7x + 7y = 12 a. ii and iii b. i and ii c. i and iv d. i and iii ____ 31. Without graphing, determine the equation whose graph intersects the graph of –4x + 3y = 10 exactly once. i) –4x + 3y = 12 ii) –16x + 12y = 40 iii) –2x + 3y = 10 a. iii b. none c. ii d. i ____ 32. Determine the number of solutions of the linear system: 3x – 7y = 43 –9x + 21y = 39 a. b. one solution no solution c. d. two solutions infinite solutions ____ 33. Determine the number of solutions of the linear system: 2x – 3y = 23 2x – 3y = 5 a. b. no solution infinite solutions c. d. two solutions one solution ____ 34. Determine the number of solutions of the linear system: 15x + 5y = 310 17x – 4y = 593 a. b. no solution one solution c. d. two solutions infinite solutions ____ 35. The first equation of a linear system is 9x + 6y = 159. Choose a second equation to form a linear system with infinite solutions. i) 9x + 6y = –318 ii) –18x – 12y = –318 iii) –18x + 6y = –318 iv) –18x + 6y = 255 a. Equation iii b. Equation iv c. Equation i d. Equation ii ____ 36. The first equation of a linear system is 7x + 12y = 158. Choose a second equation to form a linear system with exactly one solution. i) 7x + 12y = –316 ii) –14x – 24y = –316 iii) –14x + 12y = –316 iv) –14x – 24y = 0 a. Equation iii b. Equation i c. 8 Equation ii d. Equation iv Name: ________________________ ID: A ____ 37. The first equation of a linear system is –8x + 12y = –48. Choose a second equation to form a linear system with no solution. i) –8x + 12y = 240 ii) 40x – 60y = 240 iii) 40x + 12y = 240 iv) 40x + 60y = 0 a. Equation iv b. Equation ii c. Equation iii d. ____ 38. For what value of k does the linear system below have infinite solutions? 4 x + y = 11 5 kx + 2y = 22 4 8 a. 22 b. c. d. 5 5 Short Answer 39. Solve this linear system by graphing. –3x – 2y = 12 –x + y = –6 9 Equation i 0 Name: ________________________ ID: A 40. Solve this linear system by graphing. y = –2 –3x + y = 7 41. a) Write a linear system to model this situation: A hockey coach bought 20 pucks for a total cost of $47.5. The pucks used for practice cost $2.00 each, and the pucks used for games cost $2.75 each. b) Use a graph to solve this problem: How many of each type of puck did the coach purchase? 10 Name: ________________________ ID: A 42. Use substitution to solve this linear system: 5x + y = −192 −5x + 4y = 107 43. Use substitution to solve this linear system: 3 x + y = –49 4 –4x + 2y = 136 44. Create a linear system to model this situation. Then use substitution to solve the linear system to solve the problem. At the local fair, the admission fee is $6.00 for an adult and $3.50 for a youth. One Saturday, 187 admissions were purchased, with total receipts of $834.50. How many adult admissions and how many youth admissions were purchased? 45. Use an elimination strategy to solve this linear system. 6x + 6y = 618 3x − 3y = 81 46. Determine the number of solutions of this linear system. 15x + 20y = –5 17x + 11y = 286 47. For what values of k does the linear system below have: a) infinite solutions? b) one solution? c) no solution? 4 x + y = 15 5 kx + 3y = 45 Problem 48. a) Write a linear system to model this situation. Mrs. Cheechoo paid $150 for one-day tickets to Silverwood Theme Park for herself, her husband, and 2 children. Next month, she paid $405 for herself, 4 adults, and 6 children. b) Use a graph to solve this problem: What are the prices of a one-day ticket for an adult and for a child? 11 ID: A Math 10 - Unit 8 Final Review - Systems of Linear Equations Answer Section MULTIPLE CHOICE 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. A C A D A B B B A D C D B B C C B C D C C D C C A D D A B C A B A B D A D C 1 ID: A SHORT ANSWER 39. (0, –6) 40. (–3, –2) 2 ID: A 41. a) b) p + g = 20 2p + 2.75g = 47.5 The team purchased 10 pucks for practice and 10 pucks for games. 42. x = –35; y = –17 43. x = –40; y = –12 44. Let a represent the number of adult admissions, and y represent the number of youth admissions purchased. a + y = 187 6a + 3.5y = 834.5 72 adult admissions and 115 youth admissions were purchased. 45. x = 65 y = 38 46. One solution 12 47. a) k = 5 12 b) k ≠ 5 c) For the system to have no solution, the lines must be parallel; that is, their slopes are equal and their y-intercepts are different. But the lines have the same y-intercept, so they cannot be parallel. 3 ID: A PROBLEM 48. a) Let a represent the cost in dollars for a one-day adult ticket, and c represent the cost in dollars for a one-day child ticket. Then, a system of equations is: 2a + 2c = 150 5a + 6c = 405 b) Since the intersection point is at (45, 30), the cost of a one-day adult ticket is $45, and the cost of a one-day child ticket is $30. 4