Question

Solve the following pair of linear equations: px + qy = p − q, qx − py = p + q

Answer 1

px + qy = p − q … (1)

qx − py = p + q … (2)

Multiplying equation (1) by p and equation (2) by q, we obtain

p²x + pqy = p² − pq … (3)

q²x − pqy = pq + q² … (4)

Adding equations (3) and (4), we obtain

p²x + q² x = p² + q²

(p² + q²) x = p² + q²

${\displaystyle x=\frac{p^2+q^2}{p^2+q^2}=1}$

From equation (1), we obtain

p (1) + qy = p − q

qy = − q

y = − 1