828 CHAPTER 11 Systems of Equations and Inequalities 37. + = − = ⎧ ⎨ ⎪⎪⎪ ⎩ ⎪⎪⎪ x xy x xy 2 10 3 2 2 2 38. + + = + = ⎧ ⎨ ⎪⎪⎪ ⎩ ⎪⎪⎪ xy y xy y 5 13 36 0 7 6 2 2 39. + = − + = ⎧ ⎨ ⎪⎪⎪ ⎩ ⎪⎪⎪ x y x y 2 2 2 8 0 2 2 2 2 40. − + = + = ⎧ ⎨ ⎪ ⎩⎪⎪ y x x y 4 0 2 3 6 2 2 2 2 41. + = − = ⎧ ⎨ ⎪⎪⎪ ⎩ ⎪⎪⎪ x y x y 2 16 4 24 2 2 2 2 42. + = − = − ⎧ ⎨ ⎪ ⎩⎪⎪ x y x y 4 3 4 2 6 3 2 2 2 2 43. − + = + = ⎧ ⎨ ⎪⎪ ⎪⎪ ⎪ ⎩ ⎪⎪ ⎪⎪ ⎪ x y x y 5 2 3 0 3 1 7 2 2 2 2 44. − + = − + = ⎧ ⎨ ⎪⎪ ⎪⎪ ⎪ ⎩ ⎪⎪ ⎪⎪ ⎪ x y x y 2 3 1 0 6 7 2 0 2 2 2 2 45. + = − = ⎧ ⎨ ⎪⎪ ⎪⎪ ⎪ ⎩ ⎪⎪ ⎪⎪ ⎪ x y x y 1 6 6 2 2 19 4 4 4 4 46. − = + = ⎧ ⎨ ⎪⎪ ⎪⎪ ⎪ ⎩ ⎪⎪ ⎪⎪ ⎪ x y x y 1 1 1 1 1 4 4 4 4 4 47. − + = + = ⎧ ⎨ ⎪⎪⎪ ⎩ ⎪⎪⎪ x xy y x xy 3 2 0 6 2 2 2 48. − − = + + = ⎧ ⎨ ⎪⎪ ⎩ ⎪⎪ x xy y xy x 2 0 6 0 2 2 49. + + − − = + + − = ⎧ ⎨ ⎪⎪ ⎪⎪ ⎩ ⎪⎪ ⎪⎪ y y x x y x y 2 0 1 2 0 2 2 50. − + + − = − + − = ⎧ ⎨ ⎪⎪ ⎪ ⎩ ⎪⎪ ⎪⎪ x x y y x y y x 2 3 4 0 2 0 3 2 2 2 2 51. { ( ) = = y y log 3 log 4 5 x x 52. ( ) ( ) = = ⎧ ⎨ ⎪⎪ ⎩ ⎪⎪ y y log 2 3 log 4 2 x x 53. { = = + x y x y ln 4ln log 2 2log 3 3 54. { = = + x y x y ln 5ln log 3 2 log 2 2 55. Graph the equations given in Example 4. 56. Graph the equations given in Problem 49. In Problems 57–64, use a graphing utility to solve each system of equations. Express the solution(s) rounded to two decimal places. 57. = = ⎧ ⎨ ⎪⎪⎪ ⎩ ⎪⎪⎪ − y x y e x 2 3 58. = = ⎧ ⎨ ⎪⎪⎪ ⎩ ⎪⎪⎪ − y x y e x 3 2 59. + = = ⎧ ⎨ ⎪⎪⎪ ⎩ ⎪⎪⎪ x y x y 2 4 2 3 3 60. + = = ⎧ ⎨ ⎪⎪⎪ ⎩ ⎪⎪⎪ x y x y 2 4 3 2 2 61. + = = ⎧ ⎨ ⎪⎪⎪ ⎩ ⎪⎪⎪ x y xy 12 2 4 4 2 62. + = = ⎧ ⎨ ⎪⎪ ⎩ ⎪⎪ x y xy 6 1 4 4 63. { = = xy y x 2 ln 64. + = = ⎧ ⎨ ⎪⎪ ⎩ ⎪⎪ x y y x 4 ln 2 2 Mixed Practice In Problems 65–70, graph each equation and find the point(s) of intersection, if any. 65. The line + = x y2 0 and the circle ( ) ( ) − + − = x y 1 1 5 2 2 66. The line + + = x y2 6 0 and the circle ( ) ( ) + + + = x y 1 1 5 2 2 67. The circle ( ) ( ) − + + = x y 1 2 4 2 2 and the parabola + − + = y y x 4 1 0 2 68. The circle ( ) ( ) + + − = x y 2 1 4 2 2 and the parabola − − − = y y x 2 5 0 2 69. = − y x 4 3 and the circle − + + = x x y 6 1 0 2 2 70. = + y x 4 2 and the circle + + − = x x y 4 4 0 2 2 Applications and Extensions 71. The difference of two numbers is 2 and the sum of their squares is 10. Find the numbers. 72. The sum of two numbers is 7 and the difference of their squares is 21. Find the numbers. 73. The product of two numbers is 4 and the sum of their squares is 8. Find the numbers. 74. The product of two numbers is 10 and the difference of their squares is 21. Find the numbers. 75. The difference of two numbers is the same as their product, and the sum of their reciprocals is 5. Find the numbers. 76. The sum of two numbers is the same as their product, and the difference of their reciprocals is 3. Find the numbers. 77. The ratio of a to b is 2 3 . The sum of a and b is 10. What is the ratio of +a b to −b a? 78. The ratio of a to b is 4:3.The sum of a and b is 14.What is the ratio of −a b to +a b? 79. Geometry The perimeter of a rectangle is 16 inches and its area is 15 square inches. What are its dimensions? 80. Geometry An area of 52 square feet is to be enclosed by two squares whose sides are in the ratio of 2:3. Find the sides of the squares. 81. Geometry Two circles have circumferences that add up to π 12 centimeters and areas that add up to π 20 square centimeters. Find the radius of each circle. 82. Geometry The altitude of an isosceles triangle drawn to its base is 3 centimeters, and its perimeter is 18 centimeters. Find the length of its base. 83. The Tortoise and the Hare In a 21-meter race between a tortoise and a hare, the tortoise leaves 9 minutes before the hare. The hare, by running at an average speed of 0.5
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