40. Writing Let a be any real number. Will the system below always, sometimes, or never have a solution? Explain.

    y = a x y = a x + 4 table with 2 rows and 1 column , row1 column 1 , y equals eh x , row2 column 1 , y equals eh x plus 4 , end table

41. Reasoning Explain how you can use substitution to show that the system below has no solution.

    y + x = x 3 x 2 y = 4 table with 2 rows and 1 column , row1 column 1 , y plus x equals x , row2 column 1 , fraction 3 x , over 2 y end fraction . equals 4 , end table

C Challenge

42. Agriculture A farmer grows corn, tomatoes, and sunflowers on a 320-acre farm. This year, the farmer wants to plant twice as many acres of tomatoes as acres of sunflowers. The farmer also wants to plant 40 more acres of corn than of tomatoes. How many acres of each crop should the farmer plant?

43. Track and Field Michelle and Pam are running a 200-m race. Michelle runs at an average of 7.5 m/s. Pam averages 7.8 m/s, but she starts 1 s after Michelle.

    1. How long will it take Pam to catch up to Michelle?
    2. Will Pam overtake Michelle before the finish line? Explain.

Standardized Test Prep

GRIDDED RESPONSE

SAT/ACT

44. What is the value of the x-coordinate of the solution of the given system?

    2 x + 3 y = 144 y − x = 24 table with 2 rows and 1 column , row1 column 1 , 2 x plus 3 y equals 144 , row2 column 1 , y minus x equals 24 , end table

45. You are making blueberry muffins and need to buy a muffin tin and baking cups. Each package of baking cups has 50 baking cups and costs $1.25. The muffin tin costs $15. If you have $22 to spend, at most how many baking cups can you buy?
46. What is the x-intercept of 2 y − 3 x = 24 ? 2 y minus 3 x equals 24 question mark
47. An online store charges 4% of the cost of an order to cover shipping costs. How much would you pay in dollars for shipping on an order that costs $146?
48. What is the solution of the equation 2 x − 3 = 8 ? 2 x minus 3 equals 8 question mark

Mixed Review

See Lesson 6-1.

Solve each system by graphing. Tell whether the system has one solution, infinitely many solutions, or no solution.

49. y = 3 x + 3 y = x − 3 table with 2 rows and 1 column , row1 column 1 , y equals 3 x plus 3 , row2 column 1 , y equals x minus 3 , end table

50. y = x + 1 2 x + y = 10 table with 2 rows and 1 column , row1 column 1 , y equals x plus 1 , row2 column 1 , 2 x plus y equals 10 , end table

51. y = − x + 2 x + y = 3 table with 2 rows and 1 column , row1 column 1 , y equals negative x plus 2 , row2 column 1 , x plus y equals 3 , end table

See Lesson 5-6.

Find the slope of a line perpendicular to the graph of each equation.

52. y = 3 x y equals 3 x
53. y = − 1 4 x y equals negative , 1 fourth , x

54. 1 3 x − y = 2 1 third , x minus y equals 2

    Get Ready! To prepare for Lesson 6-3, do Exercises 55–57.

    See Lesson 2-4.

    Solve each equation. Check your answer.

55. 5 x + 1 = 3 x − 5 5 x plus 1 equals 3 x minus 5
56. 4 c − 7 = − c + 3 4 c minus 7 equals negative c plus 3
57. 5 k + 7 = 3 k + 10 5 k plus 7 equals 3 k plus 10

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