Question

Solve for $x$ & $y$

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

Answer 1

The given set of equations is,

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

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

Multiplying (1) by $b$ and (2) by $a$ and subtracting (2) from (1), we get:

$\left(a^2+b^2\right)y=-\left(a^2+b^2\right)$

$y=-1$

Substituting $y=-1$ in (1), we get:

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

$ax-b=a-b$

$ax=a$

$x=1$

Therefore, the solution of the given system of equations is $x=1,y=-1$.