Question

px+qy=p-q, qx-py=p+q Solve

Answer 1

( px + qy = p-q ) x (q) 1 ( qx - py = p+q ) x (p) 2
pqx + q2y = pq - q2 _pqx -p2y = p2 + pq _______________ 0 + (q2+p2)y = pq - q2 - p2 - pq
(q2 + p2)y = - (q2 + p2) y = -1
putting y =2 in 1
px + qy = p-q
px + q(-1) = p-q
px -q = p-q
px = p
x = 1

Answer 2

Hey

Given equations are :-

• px + qy = p - q ––( i )

• qx - py = p + q –– ( ii )

Multiplying eq ( i ) by p and eq ( ii ) by q ,

we get

p²x + pqy = p ( p - q )

q²x - pqy = q ( p + q )

Adding both new results we get ,

p²x + q²x = p²- pq + pq + q²

=> x ( p² + q ² ) = p² + q²

=> x = p² + q² / p² + q²

=> x = 1 .

Now ,

putting the value of x in eq ( i )

we get ,

p( 1 ) + q y = p - q

=> p + qy = p - q

=> qy = p - q - p

=> qy = - q

=> y = - q / q

=> y = - 1 .

thanks :)