C Challenge

41. Reasoning Consider the system below.

    y = gx + 3

    y = hx + 7

    1. If g ≥ h , g greater than or equal to h comma  will the system always, sometimes, or never have exactly one solution? Explain your reasoning.
    2. If g ≤ h , g less than or equal to h comma  will the system always, sometimes, or never have infinitely many solutions? Explain your reasoning.

42. Hiking Two hikers are walking along a marked trail. The first hiker starts at a point 6 mi from the beginning of the trail and walks at a speed of 4 mi/h. At the same time, the second hiker starts 1 mi from the beginning and walks at a speed of 3 mi/h.

    1. What is a system of equations that models the situation?
    2. Graph the two equations and find the intersection point.
    3. Is the intersection point meaningful in this situation? Explain.

Standardized Test Prep

SAT/ACT

43. Which ordered pair is the solution of the system?

    2 x + 3 y = − 17 2 x plus 3 y equals negative 17

    3 x + 2 y = − 8 3 x plus 2 y equals negative 8

    1. ( 2 , − 7 ) open 2 comma negative 7 close
    2. ( − 4 , 2 ) open negative 4 comma 2 close
    3. ( − 2 , − 1 ) open negative 2 comma negative 1 close
    4. ( − 4 3 , − 2 ) open . negative , 4 thirds , comma negative 2 . close

44. Which expression is equivalent to 5 ( m − 12 ) + 8 ? 5 open m minus 12 close plus 8 question mark

    6. 5 m − 68 5 m minus 68
    7. 5 m − 20 5 m minus 20
    8. 5 m − 4 5 m minus 4
    9. 5 m − 52 5 m minus 52

    Extended Response

45. The costs for parking in two different parking garages are given in the table below.

    1. What is a system of equations that models the situation?
    2. How many hours of parking would cost the same parking in either garage?
    3. If you needed to park a car for 3 h, which garage would you choose? Why?

Garage Parking Fees

Mixed Review

See Lesson 5-8.

Graph each function by translating the graph of y = | x |.

46. y = | x | − 2 y equals vertical line x vertical line negative 2
47. y = | x | − 1 y equals vertical line x vertical line negative 1
48. y = | x + 3 |

49. y = | x + 2 |

    See Lesson 5-6.

    Find the slope of a line that is parallel to the graph of the equation.

50. y = x + 3
51. y = − 1 2 x − 4 y equals negative , 1 half , x minus 4
52. 3y + 2x = 7
53. 3x = 5y + 10

Get Ready! To prepare for Lesson 6-2, do Exercises 54–57.

See Lesson 2-5.

Solve each equation for y.

54. 4x + 2y = 38
55. 1 2 x + 1 3 y = 5 1 half , x plus , 1 third , y equals 5
56. 3 2 y = 4 5 x 3 halves , y equals , 4 fifths , x
57. 1.5 x − 4.5 y = 21 1.5 x minus 4.5 y equals 21

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