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geometry

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if x+y=11, y+z=14, and x+z=13, what is the value of x+y+z ?

  • geometry -

    Eq1: X + Y = 11.

    Eq2: Y + Z = 14.
    Y = 14 - Z.

    Eq3: X + Z = 13.
    X = 13 - Z.

    In Eq1, substitute (13-Z) for X, and
    (14-Z) for Y:
    (13-Z) + (14-Z) = 11,
    13 - Z + 14 - Z = 11,
    -2Z + 27 = 11,
    -2Z = 11 - 27 = -16,
    Z = 8.

    X + Y + Z,
    Substitute 11 for y and 8 for Z:
    (X+Y)+Z = 11 + 8 = 19.

  • geometry -

    CORRECTION:
    Substitute 11 for (x+y).

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