A first number plus twice a second number is 7. Twice the first number plus the second totals 23. Fi

Discussion in 'Calculator Requests' started by math_celebrity, Sep 18, 2018.

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  1. math_celebrity

    math_celebrity Administrator Staff Member

    A first number plus twice a second number is 7. Twice the first number plus the second totals 23. Find the numbers

    Let the first number be a and the second number be b. We have:
    1. a + 2b = 7
    2. 2a + b = 23
    Rearrange (1) into (3)
    (3) a = 7 - 2b

    Substitute (3) into (2):
    2(7 - 2b) + b = 23

    Multiply through:
    14 - 4b + b = 23

    Combine like terms:
    14 - 3b = 23

    Subtract 14 from each side:
    -3b = 9

    Divide each side by -3
    b = -3

    Substitute this into (3)
    a = 7 - 2b
    a = 7 - 2(-3)
    a = 7 + 6
    a = 13

    (a, b) = (13, -3)
     

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