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Rajan@2021
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Solve for x and y: 4x+6y=3xy, 8x+9y=5xy

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This question is taken from linear equations in two variables in which we have to find the value of variables x and y from the equations 4x+6y=3xy, 8x+9y=5xy

Kindly give me a detailed solution of this question

RS Aggarwal, Class 10, chapter 3B, question no 25

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  1. The given equations are:

    4x + 6y = 3xy …..(i)

    8x + 9y = 5xy ……(ii)

    From equation (i), we have:

    4x + 6y/ xy = 3

    ⇒ 4/y + 6/x = 3 ……(iii)

    For equation (ii), we have:

    8x + 9y/ xy = 5

    ⇒ 8/y + 9/x = 5 ……(iv)

    On substituting 1/y = v and 1/x = u, we get:

    4v + 6u = 3 ……(v)

    8v + 9u = 5 …….(vi)

    On multiplying (v) by 9 and (vi) by 6, we get:

    36v + 54u = 27 ….(vii)

    48v + 54u = 30 ….(viii)

    On subtracting (vii) from (viii), we get:

    12v = 3

    ⇒ v = 3/12 = 1/4

    ⇒ 1/ y = 1/4

    ⇒ y = 4  On substituting y =4 in (iii), we get:

    4/4 + 6/x= 3

    ⇒ 1 + 6/x = 3

    ⇒ 6/x = (3 – 1) = 2

    ⇒ 2x = 6

    ⇒ x = 6/2 = 3

    Hence, the required solution is x = 3 and y = 4.

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