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Rajan@2021
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Solve the following systems of equations by using the method of cross multiplication: 1/x+1/y=7, 2/x+3/y=17

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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 1/x+1/y=7, 2/x+3/y=17 and we have to find the value of variables x and y from the given equations by using the method of cross multiplication

RS Aggarwal, Class 10, chapter 3C, question no 9

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1 Answer

  1. Simplify given equations:
    Let 1/x=u and 1/y=v

    1/x+1/y=7 implies

    u+v=7

    2/x+3/y=17 implies

    2u+3v=17

    New set of equation is:
    u+v=7...(1)
    2u+3v=17...(2)

    From equation (1):a1=1,b1=1 and c1=7
    From equation (2):a2=2,b2=3 and c2=17

    Using cross multiplication method:
    u/(−17+21​)=v/(−14+17​)=1/(32)

    u/4​=1 and v/3=1

    u=4 and q=3

    x=1/4 nad y=1/3 [Since we consider p=1/x and q=1/y]
    Answer x=1/4,y=1/3

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