850 CHAPTER 11 Systems of Equations and Inequalities In Problems 32 and 33, use properties of determinants to find the value of each determinant if it is known that = x y a b 8. 32. x y a b 2 2 33. y x b a In Problems 34–38, find the partial fraction decomposition of each rational expression. 34. ( ) − x x 6 4 35. ( ) − − x x x 4 1 2 36. ( )( ) + + x x x 9 1 2 37. ( ) + x x 4 3 2 2 38. ( )( ) + − x x x 1 1 2 2 2 In Problems 39–43, solve each system of equations. 39. + + = + = ⎧ ⎨ ⎪⎪ ⎩ ⎪⎪ x y x y 2 3 0 5 2 2 40. + = − = ⎧ ⎨ ⎪⎪⎪ ⎩ ⎪⎪⎪ xy y y xy 2 10 3 2 2 2 41. + = = ⎧ ⎨ ⎪⎪⎪ ⎩ ⎪⎪⎪ x y y x y 6 3 2 2 2 42. + + = + + = ⎧ ⎨ ⎪⎪⎪ ⎩ ⎪⎪⎪ x xy y x xy y 3 4 5 8 3 2 0 2 2 2 2 43. − + + =− − + + = ⎧ ⎨ ⎪⎪ ⎪⎪ ⎩ ⎪⎪ ⎪⎪ x x y y x x y y 3 2 1 0 2 2 2 In Problems 44 and 45 graph each inequality. 44. + ≤ x y 3 4 12 45. ≤ y x2 In Problems 46–48, graph each system of inequalities. State whether the graph is bounded or unbounded, and label the corner points. 46. − + ≤ + ≥ ⎧ ⎨ ⎪⎪ ⎩ ⎪⎪ x y x y 2 2 2 47. ≥ ≥ + ≤ + ≤ ⎧ ⎨ ⎪⎪ ⎪⎪ ⎪ ⎩ ⎪⎪ ⎪⎪ ⎪⎪ x y x y x y 0 0 4 2 3 6 48. ≥ ≥ + ≤ + ≥ ⎧ ⎨ ⎪⎪ ⎪⎪ ⎪ ⎩ ⎪⎪ ⎪⎪ ⎪⎪ x y x y x y 0 0 2 8 2 2 In Problems 49 and 50, graph each system of inequalities. 49. + ≤ + ≥ ⎧ ⎨ ⎪⎪ ⎩ ⎪⎪ x y x y 16 2 2 2 50. ≤ ≤ ⎧ ⎨ ⎪⎪ ⎩ ⎪⎪ y x xy 4 2 In Problems 51 and 52, solve each linear programming problem. 51. Maximize = + z x y 3 4 subject to the constraints ≥ ≥ + ≥ + ≤ x y x y x y 0, 0, 3 2 6, 8 52. Minimize = + z x y 3 5 subject to the constraints ≥ ≥ + ≥ + ≤ + ≤ x y x y x y x y 0, 0, 1, 3 2 12, 3 12 53. Find A so that the system of equations has infinitely many solutions. + = + = ⎧ ⎨ ⎪⎪ ⎩ ⎪⎪ x y x y A 2 5 5 4 10 54. Find A so that the system in Problem 53 is inconsistent. 55. Curve Fitting Find the quadratic function = + + y ax bx c 2 that passes through the three points ( ) ( ) 0,1 , 1,0 , and ( ) −2, 1 . 56. Blending Coffee A coffee distributor is blending a new coffee that will cost $6.90 per pound. It will consist of a blend of $6.00-per-pound coffee and $9.00-per-pound coffee.What amounts of each type of coffee should be mixed to achieve the desired blend? [Hint: Assume that the weight of the blended coffee is 100 pounds.] $6.90/lb $9.00/lb $6.00/lb 57. Cookie Orders A cookie company makes three kinds of cookies (oatmeal raisin, chocolate chip, and shortbread) packaged in small, medium, and large boxes. The small box contains 1 dozen oatmeal raisin and 1 dozen chocolate chip; the medium box has 2 dozen oatmeal raisin, 1 dozen
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