Solve each of the following systems of equations by the method of cross-multiplication :

GIVEN: 

$a x+b y=a-b$

$b x-a y=a+b$

To find: The solution of the systems of equation by the method of cross-multiplication:

Here we have the pair of simultaneous equation

$a x+b y-(a-b)=0$

$b x-a y-(a+b)=0$

By cross multiplication method we get

Therefore $x=1$ and $y=-1$

Hence we get the value of $x=1$ and $y=-1$