Question

Solve using cross - multiplication method :-

px + qy = p - q ,

qx - py = p + q


Give detailed steps. Don't use any other method to solve.

Answer 1

HELLO DEAR,

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

qx-py=p+q-----------(1)

now the cross multiplication method,

$\frac{x}{ - qp - {q}^{2} - {p}^{2} + pq } = \frac{y}{ - pq + {q}^{2} + {p}^{2} + pq } = \frac{1}{ - {p}^{2} - {q}^{2} }$
-----(1)

$\frac{x}{ - {q}^{2} - {p}^{2} } = \frac{1}{ - {p}^{2} - {q}^{2} } \\ \\ = > x = \frac{ - {p}^{2} - {q}^{2} }{ - {p}^{2} - {q}^{2} } \\ \\ = > x = 1$
-----(2)

$\frac{y}{ {q}^{2} + {p}^{2} } = \frac{1}{ - {p}^{2} - {q}^{2} } \\ \\ = > y = \frac{ {p}^{2} + {q}^{2} }{ - ( {p}^{2} + {q}^{2}) } \\ \\ = > y = - 1$

I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

Hello... bhaiya...

The given equation is 

px+qy=p-q .... i

qx-py=p+q .... ii

By cross multiplication method

x/-qp-q-p+pq = y/-pq+q+p+pq = 1/-p²-q²

x/-q²-p² = y/q²+p² = 1/-p²-q²

x/-q²-p² = 1/-p²-q² , y/q²+p² = 1/-p²-q²

x = -p²-q²/-p²-q² , y = p²+q²/-p²-q²

x = 1 and y = -1