A first number plus twice a second number is 14. Twice the first number plus the second totals 40. F

Discussion in 'Calculator Requests' started by math_celebrity, Mar 9, 2021.

  1. math_celebrity

    math_celebrity Administrator Staff Member

    A first number plus twice a second number is 14. Twice the first number plus the second totals 40. Find the numbers.

    Givens and assumptions:
    • Let the first number be x.
    • Let the second number be y.
    • Twice means multiply by 2
    • The phrases is and totals mean equal to

    We're given two equations:
    1. x + 2y = 14
    2. 2x + y = 40
    To solve this system, we can take a shortcut, and multiply the top equation by -2 to get our new system:
    1. -2x - 4y = -28
    2. 2x + y = 40
    Now add both equations together
    (-2 _ 2)x (-4 + 1)y = -28 + 40
    -3y = 12

    To solve this equation, we type it in our search engine and we get:
    y = -4

    We substitute this back into equation 1 for y = -4:
    x + 2(-4) = 14
    x - 8 = 14

    To solve this equation for x, we type it in our search engine and we get:
    x = 22
     

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