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99x + 101y = 499 ; …

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99x + 101y = 499 ; 101x + 99y = 501

    • Posted by Paras Jadhav 5 years, 7 months ago

    ICSE & ISC > Class 10 > Mathematics
    • 1 answers

    Yogita Ingle 5 years, 7 months ago

    Let us use a  trick to solve it quickly

    99x + 101y = 499 ............ i

    101x + 99y = 501............ ii

    subtract i  from  ii

    2x - 2y = 2
    x - y =1
    x = 1 + y   ........   iii

    add i and  ii

    200x + 200y = 1000
    x + y = 5 .................................. iv

    Now from iii and  iv  ,  we get  1 + y + y = 5       or          2y = 4       or        y = 2     ......  v

    again from iii and  v   , we get  x = 1 + 2 = 3

    Hence x = 3  ,  y = 2

    0Thank You

    ANSWER
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