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

p²x + q²x = p² – pq + pq + q²

`x = (p^2 + q^2)/(p^2 + q^2)`

= 1

Substituting x = 1 in (i), we have

p + qy = p – q

⇒ qy = –p

⇒ y = –1

Hence, x = 1 and y = –1.