Solve for x and y: px + qy = p – q, qx – py = p + q

1.	Solve for x and y: px + qy = p – q, qx – py = p + q
Answer» 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 = 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.

Answer»

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 = 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.

Discussion