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

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