886 CHAPTER 9 Systems and Matrices Use a graphing calculator to solve each system. Express solutions with approximations to the nearest thousandth. 43. 11 3 x + y = 0.5 0.6x - y = 3 44. 23x - y = 5 100x + y = 9 45. 27x + 22y = 3 26x - y = 23 46. 0.2x + 22y = 1 25x + 0.7y = 1 Solve each system. See Example 6. 47. x + y + z = 2 2x + y - z = 5 x - y + z = -2 48. 2x + y + z = 9 -x - y + z = 1 3x - y + z = 9 49. x + 3y + 4z = 14 2x - 3y + 2z = 10 3x - y + z = 9 50. 4x - 3y + z = 9 3x + 2y - 2z = 4 x - y + 3z = 5 51. x + 4y - z = 6 2x - y + z = 3 3x + 2y + 3z = 16 52. 4x - y + 3z = -2 3x + 5y - z = 15 -2x + y + 4z = 14 53. x - 3y - 2z = -3 3x + 2y - z = 12 -x - y + 4z = 3 54. x + y + z = 3 3x - 3y - 4z = -1 x + y + 3z = 11 55. 2x + 6y - z = 6 4x - 3y + 5z = -5 6x + 9y - 2z = 11 56. 8x - 3y + 6z = -2 4x + 9y + 4z = 18 12x - 3y + 8z = -2 57. 2x - 3y + 2z - 3 = 0 4x + 8y + z - 2 = 0 -x - 7y + 3z - 14 = 0 58. -x + 2y - z - 1 = 0 -x - y - z + 2 = 0 x - y + 2z - 2 = 0 Solve each system in terms of the arbitrary variable z. See Example 7. 59. x - 2y + 3z = 6 2x - y + 2z = 5 60. 3x - 2y + z = 15 x + 4y - z = 11 61. 5x - 4y + z = 9 y + z = 15 62. 3x - 5y - 4z = -7 y - z = -13 63. 3x + 4y - z = 13 x + y + 2z = 15 64. x - y + z = -6 4x + y + z = 7 Solve each system. State whether it is an inconsistent system or has infinitely many solutions. If a system has infinitely many solutions, write the solution set with z arbitrary. See Examples 3, 4, 6, and 7. 65. 3x + 5y - z = -2 4x - y + 2z = 1 -6x - 10y + 2z = 0 66. 3x + y + 3z = 1 x + 2y - z = 2 2x - y + 4z = 4 67. 5x - 4y + z = 0 x + y = 0 -10x + 8y - 2z = 0 68. 2x + y - 3z = 0 4x + 2y - 6z = 0 x - y + z = 0 Solve each system. (Hint: In Exercises 69–72, let 1 x = t and 1 y = u.) 69. 2 x + 1 y = 3 2 3 x - 1 y = 1 70. 1 x + 3 y = 16 5 5 x + 4 y = 5 71. 2 x + 1 y = 11 3 x - 5 y = 10
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