Question

Solve : $ax+by=a-b$
$bx-ay=a+b$

• A. $x=a,y=-b$
• B. $x=1,y=-1$
• C. $x=-1,y=1$
• D. $x=\frac{1}{a},y=-\frac{1}{b}$

Answer 1

The correct option is B $x=1,y=-1$

$ax+by=a-b$ ............ (1)

$bx-ay=a+b$ .............. (2)

Multiply equation (1) with $a$ and equation (2) with $b$ ,

$a^{2}x+aby=a^2-ab$ ................. (3)

$b^{2}x-aby=ab+b^2$ ................. (4)

Adding equation (3) and (4), we get

$a^{2}x+b^{2}x=a^2+b^2$

$(a^2+b^2)x=a^2+b^2$

$\Rightarrow x=1$

Substitute $x=1$ in equation (1),

$a\left(1\right)+by=a-b$

$by=-b$

$y=-\frac{b}{b}=-1$