\[\left( 12\frac{5}{13} + y \right) - 9\frac{9}{13} = 7\frac{7}{13}\]
\[12\frac{5}{13} + y = 7\frac{7}{13} + 9\frac{9}{13}\]
\[12\frac{5}{13} + y = 16\frac{16}{13}\]
\[y = 16\frac{16}{13} - 12\frac{5}{13}\]
\[y = 4\frac{11}{13}.\]