A basketball player scored 33 points during a game by shooting 1-point free throws, 2-point field goals, and 3-point field goals.

A basketball player scored 33 points during a game by shooting 1-point free throws, 2-point field goals, and 3-point field goals. The player scored 17 times. She scored 3 more 2-point field goals than 1-point free throws. The system of equations below represents the situation, where x is the number of 1-point free throws, y is the number of 2-point field goals, and z is the number of 3-point field goals. x + y + z = 17 x + 2y + 3z = 33 y – x = 3 Which matrix and solution represents the number of 1-point free throws, 2-point field goals, and 3-point field goals the player scored? The player scored five 1-point field goals, eight 2-point field goals, and four 3-point field goals. The player scored five 3-point field goals, eight 2-point field goals, and four 1-point field goals The player scored seven 1-point field goals, four 2-point field goals, and six 3-point field goals. The player scored seven 3-point field goals, four 2-point field goals, and six 1-point field goals.

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This Post Has 7 Comments

  1. this should help you answer ur question

    We have 4 ways of solving one-step equations: Adding, Substracting, multiplication and division.
    If we add the same number to both sides of an equation, both sides will remain equal.
    Example
    x=y

    x+z=y+z

    If we subtract the same number from both sides of an equation, both sides will remain equal.

  2. The number of 1 point throw is 5, the number of 2 point throw is 8 and the number of 3 point throw is 4

    Step-by-step explanation:

    Let x represent the number of  1-point free throws, y is the number of 2-point field goals, and z is the number of 3-point field goals. A basketball player scored 33 points during a game by shooting 1-point free throws, 2-point field goals, and 3-point field goals. Each of 1 point free throw is 1 point, each of 2 point free throw is 2 points and each of the 3 point free throw is 3 points. This is represented by the equation:

    x + 2y + 3z = 33             (1)

    Also, The player scored 17 times, therefore it is represented by:

    x + y + z = 17                   (2)

    The player scored  3 more 2-point field goals than 1-point free throws, it is represented by:

    y = x + 3                      

    -x + y = 3                         (3)

    Solving equation 1, eqn 2 and eqn 3 simultaneously:

    x = 5, y = 8, z = 4.

    The number of 1 point throw is 5, the number of 2 point throw is 8 and the number of 3 point throw is 4

  3. No. of 1 pt free throws = 5, No. of 2 pt goals = 8, No. of 3 pt goals = 4

    Step-by-step explanation:

    Equations : x + y + z = 17 [ Total times taken to score ]

    1x + 2y + 3z = 33 [ Total Score ]

    Also, y = x + 3

    Putting the value of 'y' in both equations :

    x + (x + 3)+ z = 17 → 2x + 3 + z = 17 → 2x + z = 14  (i)

    1x + 2 (x + 3) + 3z = 33 →  x + 2x + 6 + 3z = 33 → 3x + 3z = 27 (ii)

    Solving these equations :

    From (i), z = 14 - 2x

    Putting this value in (ii), 3x + 3(14 - 2x) = 27 → 3x + 42 - 6x = 27

    42 - 3x = 27 → 3x = 15 → x = 5

    y = x + 3 = 5 + 3 → y = 8

    z = 17 - x - y → z = 17 - 5 - 8 = 17 - 13 → z = 4

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