Question

Solve : $px+qy=p-q$
$qx-py=p+q$

Answer 1

$px+qy=p-q$ ............. (1)

$qx-py=p+q$ .............(2)

Multiply equation (1) with $p$ and equation (2) with $q$ ,

$p^{2}x+pqy=p^2-pq$ ........... (3)

$q^{2}x-pqy=pq+q^2$ ............ (4)

Add (3) and (4),

$p^{2}x+q^{2}x=p^2+q^2$

$x(p^2+q^2)=p^2+q^2$

$\Rightarrow x=1$

Put $x=1$ in equation (1) to get the value of $y$ ,

$p\left(1\right)+qy=p-q$

$p+qy=p-q$

$qy=-q$

$\Rightarrow y=-1$