Explanation

Put u = 1/x and v = 1/y, turning the system into pu + qv = m and qu + pv = n. Eliminating v gives (p²−q²)u = mp−nq, so u = (mp−nq)/(p²−q²), and symmetrically v = (np−mq)/(p²−q²). Hence x/y = v/u = (np−mq)/(mp−nq), option C. The other options misplace the signs and fail to satisfy the original equations.