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