71 72 73 74 Solve each system of inequalities and shade the region on a graph

# 71 72 73 74 solve each system of inequalities and

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71. 72. 73. 74. Solve each system of inequalities and shade the region on a graph, or indicate that the system has no solution. 75. 76. 77. 78. 79. 80. 11.7 Rotation of Axes The coordinates of a point in the xy -coordinate system are given. Assuming the X - and Y -axes are found by rotating the x - and y -axes by an angle , find the corresponding coordinates for the point in the XY -system. 81. ( 3, 2), 82. (4, 3), Transform the equation of the conic into an equation in X and Y (without an XY -term) by rotating the x - and y -axes through an angle . Then graph the resulting equation. 83. 84. 25 x 2 + 14 xy + 25 y 2 - 288 = 0, u = p 4 2 x 2 + 4 1 3 xy - 2 y 2 - 16 = 0, u = 30° u = 45° u = 60° y Ú 1 - x 2 y Ú x + 1 9 x 2 + 16 y 2 144 4 y 2 - 9 x 2 36 y Ú x - 1 y 10 - x 3 x 2 + 3 y 2 27 y Ú ( x + 1) 2 - 2 y x y … - x 2 + 2 x 2 + y 2 4 y Ú x 2 - 2 9 x 2 + 4 y 2 36 y Ú ln( x - 1) y 6 - x 3 + 2 y e x x 2 + y 2 7 16 y Ú x 2 + 3 x 2 + y 2 = 4 1 x 2 - 1 y 2 = - 3 x 2 + y 2 = 2 2 x 2 + 1 y 2 = 15 x 2 - 2 xy = 0 x - y = - 1 2 x 2 + 4 xy = 9 x 3 - y 3 = - 19 REVIEW EXERCISES

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