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Rajan@2021
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Solve for x and y: px+qy=p-q, qx-py=p+q

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One of the most important and conceptual question from linear equations in two variables in which we have been asked to find the value of variables x and y from the equations px+qy=p-q, qx-py=p+q

Kindly give me a detailed solution of this question

RS Aggarwal, Class 10, chapter 3B, question no 42

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  1. px+qy=p−q         …………. (1)
    qx−py=p+q          ………….(2)

    Multiply equation (1) with p and equation (2) with q ,

    p²x+pqy=p²−pq  ……….. (3)

    q²x−pqy=pq+q²  ………… (4)

    Add (3) and (4),

    p²x+q²x=p²+q²

    x(p²+q²)=p²+q²

    ⇒x=1

    Put x=1 in equation (1) to get the value of y ,

    p(1)+qy=p−q

    p+qy=p−q

    qy=−q

    ⇒y=−1

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