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March 26, 2017

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Translate the problem into a pair of linear equations in two variables. Solve the equations using either elimination or substitution. State your answer for both variables.


In a basketball game, Will scored 26 points, consisting only of three-point shots and two-point shots. He made a total of 11 shots. How many shots of each type did he make?

  • algebra - ,

    first, represent the unknown using variables:
    let x = number of 2-point shots
    let y = number of 3-point shots
    then set-up the equations. for the first statement, total score is 26, so:
    2x + 3y = 26
    for the second statement, total number of shots is 11, so:
    x + y = 11

    using substitution:
    for the 2nd equation, x + y = 11, express one of the variables in terms of the other,, in this case, i will use x:
    x + y = 11 *transpose all terms not containing x
    x = 11 - y *when transposing, the sign of the term transposed would be the opposite

    then substitute to the 1st equation:
    2x + 3y = 26
    2(11 - y) + 3y = 26
    22 - 2y + 3y = 26
    22 + y = 26
    y = 26-22 = 4
    substituting the value obtained for y on either equations: (in this case, substitute to 1st equation)
    x + y = 11
    x + 4 = 11
    x = 7

    therefore,,
    x = 7 two-point shots, and
    y = 4 three-point shots

    so there,, =)

  • algebra - ,

    4\x+@=3

  • algebra - ,

    4\x+2=3

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