Question

If ax + by = a ^2 - b^2 and bx + ay = 0 then find the value of x -
y
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Answer 1

$ax+by = a^2-b^2 \rightarrow(i)$

$bx+ay = 0 \rightarrow(ii)$

$(ii)*\frac{b}{a}$

$\frac{b^2}{a}x+by =0 \rightarrow(iii)$

$(i)-(iii)$

$x(a - \frac{b^2}{a}) = a^2-b^2$

$\frac{x(a^2-b^2)}{a} = a^2-b^2$

$x = a$

Substituting x = a in (ii)

$y = -b$

Hence,

$x = a\\ y=(-b)$

$x-y = a+b$

HOPE THIS HELPS!!