766 CHAPTER 11 Systems of Equations and Inequalities 43. + = − = + = ⎧ ⎨ ⎪⎪ ⎪⎪ ⎩ ⎪⎪ ⎪⎪ x y x z y z 9 2 13 3 2 7 44. + = − − + = − =− ⎧ ⎨ ⎪⎪ ⎪⎪ ⎩ ⎪⎪ ⎪⎪ x y y z x z 2 4 2 4 0 3 2 11 45. − + = + + = − + − =− ⎧ ⎨ ⎪⎪ ⎪⎪ ⎩ ⎪⎪ ⎪⎪ x y z x y z x y z 2 3 7 2 4 3 2 2 10 46. + − = − + + =− − − = ⎧ ⎨ ⎪⎪ ⎪⎪ ⎩ ⎪⎪ ⎪⎪ x y z x y z x y z 2 3 0 2 2 7 3 4 3 7 47. − − = + + = + = ⎧ ⎨ ⎪⎪ ⎪⎪ ⎩ ⎪⎪ ⎪⎪ x y z x y z x y 1 2 3 2 3 2 0 48. − − = − + + = − − = ⎧ ⎨ ⎪⎪ ⎪⎪ ⎩ ⎪⎪ ⎪⎪ x y z x y z x y z 2 3 0 2 5 3 4 1 49. − − = − + − =− − − = ⎧ ⎨ ⎪⎪ ⎪⎪ ⎩ ⎪⎪ ⎪⎪ x y z x y z x y z 1 2 3 4 3 2 7 0 50. − − = + + = + + = ⎧ ⎨ ⎪⎪ ⎪⎪ ⎩ ⎪⎪ ⎪⎪ x y z x y z x y z 2 3 0 3 2 2 2 5 3 2 51. − + = − + = − + − = ⎧ ⎨ ⎪⎪ ⎪⎪ ⎩ ⎪⎪ ⎪⎪ x y z x y z x y z 2 2 3 6 4 3 2 0 2 3 7 1 52. − + = − + =− − + = ⎧ ⎨ ⎪⎪ ⎪⎪ ⎩ ⎪⎪⎪⎪ x y z x y z x y z 3 2 2 6 7 3 2 1 2 3 4 0 53. + − = − + =− + − = ⎧ ⎨ ⎪⎪ ⎪⎪ ⎩ ⎪⎪ ⎪⎪ x y z x y z x y z 6 3 2 5 3 2 14 54. − + = − − + =− + − = ⎧ ⎨ ⎪⎪ ⎪⎪ ⎩ ⎪⎪ ⎪⎪ x y z x y z x y z 4 2 3 4 15 5 2 12 55. + − =− − + =− − + − = ⎧ ⎨ ⎪⎪ ⎪⎪ ⎩ ⎪⎪ ⎪⎪ x y z x y z x y z 2 3 2 4 7 2 2 3 4 56. + − =− − + = + + = ⎧ ⎨ ⎪⎪ ⎪⎪ ⎩ ⎪⎪ ⎪⎪ x y z x y z x y z 4 3 8 3 3 12 6 1 In Problems 19–56, solve each system of equations. If the system has no solution, state that it is inconsistent. For Problems 19–30, graph the lines of the system. 19. + = − = ⎧ ⎨ ⎪⎪ ⎩ ⎪⎪ x y x y 8 4 20. + =− + =− ⎧ ⎨ ⎪⎪ ⎩ ⎪⎪ x y x y 2 7 3 21. x y x y 5 21 2 3 12 − = + =− ⎧ ⎨ ⎪⎪ ⎩ ⎪⎪ 22. + = − =− ⎧ ⎨ ⎪⎪ ⎩ ⎪⎪ x y x y 3 5 2 3 8 23. = + = ⎧ ⎨ ⎪⎪ ⎩⎪⎪ x x y 3 24 2 0 24. + =− − =− ⎧ ⎨ ⎪⎪ ⎩ ⎪⎪ x y y 4 5 3 2 8 25. − = + = ⎧ ⎨ ⎪⎪ ⎩ ⎪⎪ x y x y 3 6 2 5 4 1 26. + = − =− ⎧ ⎨ ⎪⎪ ⎪ ⎩ ⎪⎪ ⎪ x y x y 2 4 2 3 3 5 10 27. + = + = ⎧ ⎨ ⎪⎪ ⎩ ⎪⎪ x y x y 2 1 4 2 3 28. − = − + = ⎧ ⎨ ⎪⎪ ⎩ ⎪⎪ x y x y 5 3 3 2 29. − = + = ⎧ ⎨ ⎪⎪ ⎩ ⎪⎪ x y x y 2 0 4 2 12 30. + =− + = ⎧ ⎨ ⎪⎪ ⎪ ⎩ ⎪⎪ ⎪ x y x y 3 3 1 4 8 3 3 1. + = + = ⎧ ⎨ ⎪⎪ ⎩ ⎪⎪ x y x y 2 4 2 4 8 32. − = − = ⎧ ⎨ ⎪⎪ ⎩ ⎪⎪ x y x y 3 7 9 3 21 33. − =− + = ⎧ ⎨ ⎪⎪ ⎩ ⎪⎪ x y x y 2 3 1 10 11 34. − = + = ⎧ ⎨ ⎪⎪ ⎩ ⎪⎪ x y x y 3 2 0 5 10 4 35. + = − = ⎧ ⎨ ⎪⎪ ⎪ ⎩ ⎪⎪ ⎪ x y x y 2 3 6 1 2 36. + =− − = ⎧ ⎨ ⎪⎪ ⎪ ⎩ ⎪⎪ ⎪ x y x y 1 2 2 2 8 37. + = − =− ⎧ ⎨ ⎪⎪ ⎪⎪⎪ ⎩ ⎪⎪ ⎪⎪ ⎪ x y x y 1 2 1 3 3 1 4 2 3 1 38. − =− + = ⎧ ⎨ ⎪⎪ ⎪⎪⎪ ⎩ ⎪⎪ ⎪⎪ ⎪ x y x y 1 3 3 2 5 3 4 1 3 11 39. − = − = ⎧ ⎨ ⎪⎪ ⎩ ⎪⎪ x y x y 3 6 7 5 2 5 40. − =− + = ⎧ ⎨ ⎪⎪ ⎪ ⎩ ⎪⎪ ⎪ x y x y 2 1 1 2 3 2 41. + = − = ⎧ ⎨ ⎪⎪ ⎪⎪ ⎪ ⎩ ⎪⎪ ⎪⎪ ⎪ x y x y 1 1 8 3 5 0 42. − = + = ⎧ ⎨ ⎪⎪ ⎪⎪ ⎪ ⎩ ⎪⎪ ⎪⎪ ⎪ x y x y 4 3 0 6 3 2 2 [Hint: Let = u x 1 and = v y 1 , and solve for u and v. Then = x u 1 and = ⎤ ⎦ ⎥ y v 1 . Applications and Extensions 57. The perimeter of a rectangular floor is 90 feet. Find the dimensions of the floor if the length is twice the width. 58. The length of fence required to enclose a rectangular field is 3000 meters. What are the dimensions of the field if it is known that the difference between its length and width is 50 meters? 59. Orbital Launches In 2022, SpaceX set a record with 61 orbital launches. The launches were either for the Starlink project or for other customers (including NASA). The number of Starlink launches was 10 more than half the number of orbital launches for other customers. Determine the number of orbital launches for Starlink and for other customers in 2022. Source: Federal Aviation Administration. 60. Movie Theater Tickets A movie theater charges $9.00 for adults and $7.00 for senior citizens. On a day when 325 people paid for admission, the total receipts were $2495. How many who paid were adults? How many were seniors? 61. Mixing Nuts A store sells cashews for $5.00 per pound and peanuts for $1.50 per pound. The manager decides to mix 30 pounds of peanuts with some cashews and sell the mixture for $3.00 per pound. How many pounds of cashews should be mixed with the peanuts so that the mixture will produce the same revenue as selling the nuts separately?
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