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Solve the following systems of equations by using the method of cross multiplication: 5/(x+y)-2/(x-y)+1=0, 15/(x+y)+7/(x-y)-10=0

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Sir please give me a detailed solution of this question as it was already asked in various important examinations in which we have given two equations 5/(x+y)-2/(x-y)+1=0, 15/(x+y)+7/(x-y)-10=0 and we have been asked to find the value of variables x and y by using the method of cross multiplication

RS Aggarwal, Class 10, chapter 3C, question no 10


1 Answer

  1. Substitute 1/(x+y)=a and  1/(xy)=b

    We get equations as follows: 5a2b+1=0 and 15a+7b10=0

    Using method of cross-multiplication we get:



    From a/13=1/65 we get a=1/5

    Similarly b=1

    Resubstituting values of a and b we get x+y=5 and xy=1

    Adding these 2 equations gives us x=3 .

    Substracting 2nd equation from 1st gives us y=2

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