The given equations are
px + qy = p – q ………(i)
qx – py = p + q ………(ii)
Multiplying (i) by p and (ii) by q and adding them , we get
p2 x + q2 x = p2 – pq + pq + q2
x = p2 + q2 / p2 + q2 = 1
Substituting x = 1 in (i), we have
p + qy = p – q
⇒qy = -p
⇒y = -1
Hence, x = 1 and y = -1.