Question

Question 7 (i)
Solve the following pair of linear equations.
(i) px + qy = p − q
qx − py = p + q

Answer 1

$\left(i\right)px+qy=p-q\cdots \left(1\right)qx-py=p+q\cdots \left(2\right)$
Multiplying equation (1) by p and equation (2) by q, we obtain
$p^{2}x+pqy=p^2-pq\cdots \left(3\right)q^{2}x-pqy=pq+q^2\cdots \left(4\right)$
Adding equations (3) and (4), we obtain
$p^{2}x+q^{2}x=p^2+q^2(p^2+q^2)x=p^2+q^2$
$x=\frac{p^2+q^2}{p^2+q^2}$ =1
From equation (1), we obtain
$p\left(1\right)+qy=p-qqy=-qy=-1$