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Rajan@2021
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Solve for x and y: a²x+b²y=c², b²x+a²y=d²

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This is the basic and conceptual question from linear equations in two variables in which we have given two equations a²x+b²y=c², b²x+a²y=d² and we have been asked to find the value of variables x and y from the given equations

Kindly solve the equations

RS Aggarwal, Class 10, chapter 3B, question no 49

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3 Answers

  1. Sol:
    The given equations are
    a
    2
    x + b2
    y = c2
    ………(i)
    b
    2
    x + a2
    y = d2
    ………(ii)
    Multiplying (i) by a2
    and (ii) by b2
    and subtracting, we get
    a
    4
    x – b
    4
    x = a2
    c
    2
    – b
    2
    d
    2
    ⇒x =
    𝑎
    2𝑐
    2−𝑏
    2𝑑
    2
    𝑎4− 𝑏4
    Now, multiplying (i) by b2
    and (ii) by a2
    and subtracting, we get
    b
    4
    y – a
    4
    y = b2
    c
    2
    – a
    2
    d
    2
    ⇒y =
    𝑏
    2𝑐
    2−𝑎
    2𝑑
    2
    𝑏4− 𝑎4
    Hence, x = 𝑎
    2𝑐
    2−𝑏
    2𝑑
    2
    𝑎4− 𝑏4
    and y = 𝑏
    2𝑐
    2−𝑎
    2𝑑
    2
    𝑏4− 𝑎4
    .

    • 0
  2. Solve for x and y:
    a
    2
    x + b2
    y = c2
    , b2
    x + a2
    y = d2
    Sol:
    The given equations are
    a
    2
    x + b2
    y = c2
    ………(i)
    b
    2
    x + a2
    y = d2
    ………(ii)
    Multiplying (i) by a2
    and (ii) by b2
    and subtracting, we get
    a
    4
    x – b
    4
    x = a2
    c
    2
    – b
    2
    d
    2
    ⇒x =
    𝑎
    2𝑐
    2−𝑏
    2𝑑
    2
    𝑎4− 𝑏4
    Now, multiplying (i) by b2
    and (ii) by a2
    and subtracting, we get
    b
    4
    y – a
    4
    y = b2
    c
    2
    – a
    2
    d
    2
    ⇒y =
    𝑏
    2𝑐
    2−𝑎
    2𝑑
    2
    𝑏4− 𝑎4
    Hence, x = 𝑎
    2𝑐
    2−𝑏
    2𝑑
    2
    𝑎4− 𝑏4
    and y = 𝑏
    2𝑐
    2−𝑎
    2𝑑
    2
    𝑏4− 𝑎4
    .

    • -1
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