so I have this function:
$$f(x,y) = (ax+by, cx+dy)$$

I was wondering how you would find the inverse for this function. I know it is defined to $$f^{-1}(x,y)=\biggl(\frac{dx-by}{ad-bc}, \frac{-cx+ay}{ad-bc}\biggr)$$ when $ad-bc\neq0$ but I have no idea how this was calculated or solved other than it being written within the solution manual of a problem that involves taking the inverse. Some help would be appreciated.