Question

Solve the following pair of linear equations :

$\begin{array}{c}px+qy=p-q\\ qx-py=p+q\end{array}$

Answer 1

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

Multiplying by $p$ on both sides,

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

$qx-py=p+q$ ......(3)

Multiplying by $q$ on both sides,

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

On adding equation (2) and (4), we get

$p^{2}x+pqy+q^{2}x-pqy=p^2-pq+pq+q^2$

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

$x=1$

Substituting the value of $x$ in equation (1), we get-

$p\times 1+qy=p-q$

$qy=-q$

$y=-1.$

Hence,

$x=1,y=-1$ is the final solution of the given equation.