solving systems of equations with x and y in the denominator

[oilogoi]

I am tutoring someone and the book they are using insists they solve the system below using substitution. It is a piece of cake using elimination, but with substitution I get stuck. Any help out there?

1/x = 7 - 1/y

3/x - 1/y = 1

Thanks!

[snowdrifter]

From equation 1: (1/x - 7) = -1/y

So equation 2 becomes: 3/x + (1/x - 7) = 1
--> 4/x - 7 = 1

etc.