CAYLEY 2011 Problem 21

Suppose that x and y are positive numbers with

\begin{aligned} x y & =\frac{1}{9} \\ x(y+1) & =\frac{7}{9} \\ y(x+1) & =\frac{5}{18} \end{aligned}

What is the value of (x+1)(y+1)?

Answer Choices
A. \frac{11}{6}
B. \frac89
C. \frac{16}{9}
D. \frac{10}{9}
E. \frac{35}{18}