Multiplying p to equation (1)  and q to equation (2), we get

p²x + pqy = p² − pq ………… (iii)

q²x − pqy = pq + q² ………… (iv)

Adding equation (iii) and equation (iv),we get

p²x + q² x = p²  + q²

(p² + q² ) x = p² + q²

x = (p² + q²)/ p² + q² = 1

From equation (i), we get

p(1) + qy = p – q

qy = p-q-p

qy = -q

y = -1