260 Chapter 3 Systems of Linear Equations and Inequalities 1 10 1 2 8 5 54. 55. 56. 4x 3y 4x 2y 6 x 1 2 y 3 2 1 4 11 2 x y x y x 2 4 3 y 57. A Lincoln Town Car gets 16 mpg in the city and 24 mpg on the highway.A Lincoln Navigator gets 14 mpg in the city and 20 mpg on the highway. Suppose that each vehicle travels c miles in the city and h miles on the highway.The Town Car uses 12 gal of gasoline and the Navigator uses 14 gal. Solve the system of equations to determine the number of city and number of highway miles driven. (Source: www.fueleconomy.gov) Town Car: Navigator: 1 16 1 14 c c 1 24 1 20 h 12 h 14 58. A Subaru Forester gets 21 mpg in the city and 27 mpg on the highway.A Jeep Liberty gets 15 mpg in the city and 21 mpg on the highway. Suppose that each vehicle travels c miles in the city and h miles on the highway. The Subaru uses 12 gal of gasoline and the Jeep uses 16 gal. Solve the system of equations to determine the number of city and number of highway miles driven. Subaru: Jeep: 1 21 1 15 c c 1 27 1 21 h 12 h 16 Expanding Your Skills Sometimes the solution to a system of equations is an ordered pair containing fractions. In such a case, it is often easier to solve for each coordinate separately using the addition method.That is, use the addition method to solve for x.Then, rather than substituting x back into one of the original equations, repeat the addition method and solve for y. For Exercises 59–61, solve each system. 59. 9x 11y 47 60. 6x 7y 4 61. 4x 10y 19 5x 3y 23 4x 9y 31 5x 12y 41 Problem Recognition Exercises Solving Systems of Linear Equations For Exercises 1–4, solve each system by using three different methods. a. Use the graphing method. b. Use the substitution method. c. Use the addition method. 1. 3x y 2 2. 3x 2y 4 3. 5x 2y 4. 2y 3x 1 2 3 For Exercises 5–8, solve the system of equations by using the most efficient method. 5. y4x 9 6. 5x 2y17 7. 5x 3y 2 8. 8x 3y29 x 5y 2 7x 4y30 3 4 x 1 3 y 13 6 1 10 x 2 5 y 3 5 4x 4 y 5 2 x y x 1 4 3 4x y 4
miller_intermediate_algebra_4e_ch1_3
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