Question

If $bx+ay=a^2+b^2$ and $ax-by=0$, then the value of $(x-y)$ is

• A. $a-b$
• B. $b-a$
• C. $a^2-b^2$
• D. $b^2+a^2$

Answer 1

Answer: (B)

$b-a$

Given equations are
$bx+ay=a^2+b^2.....\left(1\right)$
$ax-by=0.....\left(2\right)$
Multiplying equation (1) by $a$ and equation (2) by $b$
$abx+a^{2}y=a^3+a{b}^2$ .....(3)
$abx-b^{2}y=0$ ......(4)
Subtracting (4) from (3), we get
$(a^2+b^2)y=a(a^2+b^2)$
$\Rightarrow y=a$
Put this value in (2), we get
$x=b$
$\Rightarrow x-y=b-a$