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Rajan@2021
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Solve: 3/(x+y) + 2/(x-y) = 2 and 9/(x+y) – 4/(x-y) = 1

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This question is taken from linear equations in two variables in which we have been asked to find the value of 3/(x+y) + 2/(x-y) = 2 and 9/(x+y) – 4/(x-y) = 1

RS Aggarwal, Class 10, chapter 3F, question no 21

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  1. Let 1/(x+y)=X and 1/(x−y)​=Y
    3X+2Y=2                       …(i)
    9X−4Y=1                        …(ii)

    On multiplying (i) by 3 and (ii) by 1 and subtracting, we get
    9X+6Y=6
    −9​X+−​4Y=−1​​
    10Y=5

    ∴Y=1/2​

    On putting Y=1/2 in (i), we get
    3X+2×1/2​=2
    ⇒X=1/3​
    ∴1/(x+y)=1/3​ and 1/(x−y)​=1/2​

    ⇒x+y=3                  …(iii)
    x−y=2                       …(iv)

    On adding (iii) and (iv), we get
    2x=5
    ⇒x=5/2​

    On putting x=25​ in (iii), we get

    5/2​+y=3
    ⇒y=3−5/2​=1/2​

    ∴x=5/2​, y=1/2​

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