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Solve for x and y: 2x+5y=8/3, 3x-2y=5/6

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This is the basic 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 2x+5y=8/3, 3x-2y=5/6

RS Aggarwal, Class 10, chapter 3B, question no 11

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  1. The given equations are:

    2x – 5y = 8/3 …..(i)

    3x – 2y = 5/6 ……..(ii)

    On multiplying (i) by 2 and (ii) by 5, we get:

    4x – 10y = 16/3 ……(iii)

    15x – 10y = 25/6 ……(iv)

    On adding (iii) and (iv), we get:

    19x = 57/ 6

    ⇒x = 57/ (6 × 19) = 3/6 = 1/2

    On substituting x = 1/2 in (i), we get:

    2 × 1/2 + 5y = 8/3

    ⇒ 5y = ( 8/3 − 1) = 5/3

    ⇒y = 5/ (3 × 5) = 1/3

    Hence, the solution is

    x = 1/2 and y = 1/3

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