Question

Solve for x and y:

px + qy = p – q,

qx – py = p + q

Answer 1

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.