986 CHAPTER 9 Systems and Matrices Find the partial fraction decomposition for each rational expression. 49. 2 3x2 - 5x + 2 50. 11 - 2x x2 - 8x + 16 51. 5 - 2x 1x2 + 221x - 12 52. x3 + 2x2 - 3 x4 - 4x2 + 4 Solve each nonlinear system of equations. 53. y = 2x + 10 x2 + y = 13 54. x2 = 2y - 3 x + y = 3 55. x2 + y2 = 17 2x2 - y2 = 31 56. 2x2 + 3y2 = 30 x2 + y2 = 13 57. xy = -10 x + 2y = 1 58. xy + 2 = 0 y - x = 3 59. x2 + 2xy + y2 = 4 x - 3y = -2 60. x2 + 2xy = 15 + 2x xy - 3x + 3 = 0 61. 2x2 - 3y2 = 18 2x2 - 2y2 = 14 Solve each problem. 62. Find all values of b such that the straight line 3x - y = b touches the circle x2 + y2 = 25 at only one point. 63. Do the circle x2 + y2 = 144 and the line x + 2y = 8 have any points in common? If so, what are they? 64. Find the equation of the line passing through the points of intersection of the graphs of x2 + y2 = 20 and x2 - y = 0. Graph the solution set of each system of inequalities. 65. x + y … 6 2x - y Ú 3 66. y … 1 3 x - 2 y2 … 16 - x2 67. Connecting Graphs with Equations Determine the system of inequalities illustrated in the graph. Write each inequality in standard form. 0 x y –2 1 1 4 –1 68. Maximize the objective function 2x + 4y for the following constraints. x Ú 0 y Ú 0 3x + 2y … 12 5x + y Ú 5 Solve each equation. 47. 2 3x -x 7 42 = 8 48. 3 6x 1 x 2 5 2 0 3 -13 = 2x
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