B Apply

43. Think About a Plan Suppose you have a part-time job delivering packages. Your employer pays you a flat rate of $9.50 per hour. You discover that a competitor pays employees $2 per hour plus $3 per delivery. How many deliveries would the competitor's employees have to make in four hours to earn the same pay you earn in a four-hour shift?
    • How can you write a system of equations to model this situation?
    • Which method should you use to solve the system?
    • How can you interpret the solution in the context of the problem?

Solve each system.

44. { 5 x + y = 0 5 x + 2 y = 30 left brace . table with 2 rows and 1 column , row1 column 1 , 5 x plus y equals 0 , row2 column 1 , 5 x plus 2 y equals 30 , end table
45. { 2 m = − 4 n − 4 3 m + 5 n = − 3 left brace . table with 2 rows and 1 column , row1 column 1 , 2 m equals negative 4 n minus 4 , row2 column 1 , 3 m plus 5 n equals negative 3 , end table
46. { 7 x + 2 y = − 8 8 y = 4 x left brace . table with 2 rows and 1 column , row1 column 1 , 7 x plus 2 y equals negative 8 , row2 column 1 , 8 y equals 4 x , end table
47. { 2 m + 4 n = 10 3 m + 5 n = 11 left brace . table with 2 rows and 1 column , row1 column 1 , 2 m plus 4 n equals 10 , row2 column 1 , 3 m plus 5 n equals 11 , end table
48. { − 6 = 3 x − 6 y 4 x = 4 + 5 y left brace . table with 2 rows and 1 column , row1 column 1 , negative 6 equals 3 x minus 6 y , row2 column 1 , 4 x equals 4 plus 5 y , end table
49. { x 3 + 4 y 3 = 300 3 x − 4 y = 300 left brace . table with 2 rows and 1 column , row1 column 1 , x over 3 , plus , fraction 4 y , over 3 end fraction , equals 300 , row2 column 1 , 3 x minus 4 y equals 300 , end table
50. { 0.02 a − 1.5 b = 4 0.5 b − 0.02 a = 1.8 left brace . table with 2 rows and 1 column , row1 column 1 , 0.02 , eh minus 1.5 b equals 4 , row2 column 1 , 0.5 b minus , 0.02 , eh equals 1.8 , end table
51. { 4 y = 2 x 2 x + y = x 2 + 1 left brace . table with 2 rows and 1 column , row1 column 1 , 4 y equals 2 x , row2 column 1 , 2 x plus y equals , x over 2 , plus 1 , end table
52. { 1 2 x + 2 3 y = 1 3 4 x − 1 3 y = 2 left brace . table with 2 rows and 1 column , row1 column 1 , 1 half , x plus , 2 thirds , y equals 1 , row2 column 1 , 3 fourths , x minus , 1 third , y equals 2 , end table

53. Error Analysis Identify and correct the error shown in finding the solution of { 3 x − 4 y = 14 x + y = − 7 left brace . table with 2 rows and 1 column , row1 column 1 , 3 x minus 4 y equals 14 , row2 column 1 , x plus y equals negative 7 , end table  using substitution.

    
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54. Break-Even Point Jenny's Bakery sells carrot muffins at $2 each. The electricity to run the oven is $120 per day and the cost of making one carrot muffin is $1.40. How many muffins need to be sold each day to break even?
55. Open-Ended Write a system of equations in which both equations must be multiplied by a number other than 1 or − 1 negative 1  before using elimination. Solve the system.
56. Chemistry A scientist wants to make 6 milliliters of a 30% sulfuric acid solution. The solution is to be made from a combination of a 20% sulfuric acid solution and a 50% sulfuric acid solution. How many milliliters of each solution must be combined to make the 30% solution?
57. Writing Explain how you decide whether to use substitution or elimination to solve a system.
58. The equation 3 x − 4 y = 2 3 x minus 4 y equals 2  and which equation below form a system with no solutions?
    1. 2 y = 1 . 5 x − 2 2 y equals 1 . 5 x minus 2
    2. 2 y = 1 . 5 x − 1 2 y equals 1 . 5 x minus 1
    3. 3 x + 4 y = 2 3 x plus 4 y equals 2
    4. 4 y − 3 x = − 2 4 y minus 3 x equals negative 2

For each system, choose the method of solving that seems easier to use. Explain why you made each choice. Solve each system.

59. { 3 x − y = 5 y = 4 x + 2 left brace . table with 2 rows and 1 column , row1 column 1 , 3 x minus y equals 5 , row2 column 1 , y equals 4 x plus 2 , end table
60. { 2 x − 3 y = 4 2 x − 5 y = − 6 left brace . table with 2 rows and 1 column , row1 column 1 , 2 x minus 3 y equals 4 , row2 column 1 , 2 x minus 5 y equals negative 6 , end table
61. { 6 x − 3 y = 3 5 x − 5 y = 10 left brace . table with 2 rows and 1 column , row1 column 1 , 6 x minus 3 y equals 3 , row2 column 1 , 5 x minus 5 y equals 10 , end table

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