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Rajan@2021
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Solve for x and y: 5/(x+y)-2/(x-y)=-1, 15/(x+y)+7/(x-y)=10

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One of the most important and conceptual question from linear equations in two variables in which we have been asked to find the value of variables x and y from the equations 5/(x+y)-2/(x-y)=-1, 15/(x+y)+7/(x-y)=10

Kindly give me a detailed solution of this question

RS Aggarwal, class 10, chapter 3B, question no 27

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  1. The given equations are

    5/ x+y – 2/ x-y = -1 ……(i)

    15/ x+y – 7/x-y= 10 ……(ii)  Substituting 1/x+y = u and 1/x-y = v in (i) and (ii), we get

    5u – 2v = -1 ……..(iii)

    15u + 7v = 10 …….(iv)

    Multiplying (iii) by 3 and subtracting it from (iv), we get

    7v + 6v = 10 + 3

    ⇒13v = 13

    ⇒v = 1

    ⇒x – y = 1 (∵ 1/ x-y = ) …..(v)

    Now, substituting v = 1 in (iii), we get

    5u – 2 = -1

    ⇒5u = 1

    ⇒u = 1/ 5

    x + y = 5 …….(vi)

    Adding (v) and (vi), we get

    2x = 6

    ⇒ x = 3

    Substituting x = 3 in (vi), we have

    3 + y = 5

    ⇒ y = 5 – 3

    = 2

    Hence, x = 3 and y = 2.

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