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Math Help - Solve with the elimination method

  1. #1
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    Solve with the elimination method

    I'm having trouble solving the following (ending up with an ordered pair) via the elimination method:
    1) 0.05x + 0.25y = 44
    2) 0.15x + 0.05y = 48

    After multiplying by 100 to lose the decimals, I then multiplied the top equation by 15 and the bottom by 5. Is that correct ( 1) 75x + 35y = 660 2)75x + 25y = 240.)?
    Then do I add the equations??

    Thanks for the help!
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  2. #2
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    You don't have to multiply by 100, just multiply the second equation by 5 to make 0.25y then eliminate
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  3. #3
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    1. 0.2x + y = 176, i.e. y = 176 - 0.2x.
    2. 3x + y = 960, i.e. y = 960 - 3x.
    ∴ 176 - 0.2x = 960 - 3x, i.e. 3x - 0.2x = 960 - 176.
    3x - 0.2x = 2.8x and 960 - 176 = 784, i.e. 2.8x = 784.
    x = 784/2.8 = 7840/28 = 1960/7 = 280
    y = 960 - 3(280) = 960 - 840 = 120
    ∴ (x, y) = (280, 120)
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