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15 February, 02:14

The sum of three numbers is 16. The sum of the first number and the second number is 2 more than the third number. The second number minus the sum of the first number and third number is twice the third number.

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  1. 15 February, 05:17
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    x = - 6, y = 15 and z = 7.

    Step-, by-step explanation:

    x + y + z = 16

    x + y = z + 2

    y - (x + z) = 2z

    Rearranging into the same form:

    x + y + z = 16 A

    x + y - z = 2 B

    -x + y - 3z = 0 C

    Subtracting A - B to eliminate x and y:

    2z = 14

    z = 7.

    Substitute z = 7 in equations B and C:

    x + y - 7 = 2

    -x + y - 3 (7) = 0

    Adding these 2 equations to eliminate x:

    2y - 28 = 2

    2y = 30

    y = 15.

    Finally substitute for y and z in equation A to find x:

    x + 7 + 15 = 16

    x = 16 - 22

    x = - 6.
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