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26 July, 18:16

the sum of two numbers is 18. twice the first number increased by three times the second number equals 40. find the numbers

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  1. 26 July, 18:40
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    4 and 14

    Step-by-step explanation:

    :the sum of two numbers is 18" can be written as

    x + y = 18 let x represent the first number, and y the second

    "twice the first number increased by three times the second number equals 40" can be written as

    2x + 3y = 40

    Now solve this system. Using elimination will probably be the easier method ...

    1. x + y = 18

    2. 2x + 3y = 40

    Multiply equation 1 by - 2 so the x variable will be the opposite of the x variable on equation 2.

    1. - 2x - 2y = - 36

    2. 2x + 3y = 40

    Now add the equations together, cancelling out 'x'

    y = 4 (2x + (-2x) = 0, so 'x' is gone, 3y + (-2y) = y, 40 + (-36) = 4)

    Since y = 4, plug that into either equation 1 or 2 and solve for x

    1. x + 4 = 18 (y becomes 4)

    x = 14 (subtract 4 on both sides to isolate 'x')
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