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Solve for x and y: 5/x+6y=13, 3/x+4y=7

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One of the most important and conceptual question from linear equations in two variables in which we have to find the value of variables x and y from the equations 5/x+6y=13, 3/x+4y=7

RS Aggarwal, Class 10, chapter 3B, question no 18

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  1. The given equations are:

    5/x + 6y = 13 ……..(i)

    3/x + 4y = 7 ……..(ii)

    Putting 1/x = u, we get:

    5u + 6y = 13 …….(iii)

    3u + 4y = 7 ……(iv)

    On multiplying (iii) by 4 and (iv) by 6, we get:

    20u + 24y = 52 ……..(v)

    18u + 24y = 42 ……..(vi)

    On subtracting (vi) from (v), we get:  2u = 10

    ⇒ u = 5

    ⇒ 1/x = 5

    ⇒ x = 1/5

    On substituting x = 1/5 in (i), we get:

    5/ 1/3 ⁄ + 6y = 13

    25 + 6y = 13

    6y = (13 – 25) = -12

    y = -2

    Hence, the required solution is

    x = 1/5 and y = -2

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