917 9.3 Determinant Solution of Linear Systems Use Cramer’s rule to solve each system of equations. If D= 0, then use another method to determine the solution set. See Examples 5–7. 63. x + y = 4 2x - y = 2 64. 3x + 2y = -4 2x - y = -5 65. 4x + 3y = -7 2x + 3y = -11 66. 4x - y = 0 2x + 3y = 14 67. 5x + 4y = 10 3x - 7y = 6 68. 3x + 2y = -4 5x - y = 2 69. 1.5x + 3y = 5 2x + 4y = 3 70. 12x + 8y = 3 1.5x + y = 0.9 71. 3x + 2y = 4 6x + 4y = 8 72. 4x + 3y = 9 12x + 9y = 27 73. 1 2 x + 1 3 y = 2 3 2 x - 1 2 y = -12 74. - 3 4 x + 2 3 y = 16 5 2 x + 1 2 y = -37 75. 2x - y + 4z = -2 3x + 2y - z = -3 x + 4y + 2z = 17 76. x + y + z = 4 2x - y + 3z = 4 4x + 2y - z = -15 77. x + 2y + 3z = 4 4x + 3y + 2z = 1 -x - 2y - 3z = 0 78. 2x - y + 3z = 1 -2x + y - 3z = 2 5x - y + z = 2 79. -2x - 2y + 3z = 4 5x + 7y - z = 2 2x + 2y - 3z = -4 80. 3x - 2y + 4z = 1 4x + y - 5z = 2 -6x + 4y - 8z = -2 81. 4x - 3y + z + 1 = 0 5x + 7y + 2z + 2 = 0 3x - 5y - z - 1 = 0 82. 2x - 3y + z - 8 = 0 -x - 5y + z + 4 = 0 3x - 5y + 2z - 12 = 0 83. 5x - y = -4 3x + 2z = 4 4y + 3z = 22 84. 3x + 5y = -7 2x + 7z = 2 4y + 3z = -8 85. x + 2y = 10 3x + 4z = 7 -y - z = 1 86. 5x - 2y = 3 4y + z = 8 x + 2z = 4 (Modeling) Solve each problem. 87. Roof Trusses The simplest type of roof truss is a triangle. The truss shown in the figure is used to frame roofs of small buildings. If a 100-pound force is applied at the peak of the truss, then the forces or weights W1 and W2 exerted parallel to each rafter of the truss are determined by the following linear system of equations. 23 2 1W1 + W22 = 100 W1 - W2 = 0 100 lb 608 608 W2 W1 Solve the system to find W1 and W2. (Data from Hibbeler, R., Structural Analysis, Fourth Edition. Copyright © 1999. Reprinted by permission of Pearson Education, Inc., New York, NY.)
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