This problem from Serge Lang’s *Basic Mathematics* in Chapter 2, question 9a.

Let a,b,c,d be numbers such that ad-bc =/= 0. Solve the following systems of equations for x and y in terms of a,b,c,d.

a] ax + by = 1, cx + dy = 2

I’m fine with solving these sorts of equations with numbers in place of a,b,c,d but trying to solve it with just variables has been a problem. I assume that the information “ad-bc =/= 0” is some sort of hint, possibly that I’m able to divide by ad-bc at some point but I don’t know how to apply it.