Решим уравнение:
$$(12 \frac{5}{13} + y) - 9 \frac{9}{13} = 7 \frac{7}{13}$$
$$12 \frac{5}{13} + y = 7 \frac{7}{13} + 9 \frac{9}{13}$$
$$12 \frac{5}{13} + y = 16 \frac{7+9}{13}$$
$$12 \frac{5}{13} + y = 16 \frac{16}{13}$$
$$12 \frac{5}{13} + y = 17 \frac{3}{13}$$
$$y = 17 \frac{3}{13} - 12 \frac{5}{13}$$
$$y = 16 \frac{16}{13} - 12 \frac{5}{13}$$
$$y = 4 \frac{16-5}{13}$$
$$y = 4 \frac{11}{13}$$
Ответ: $$y = 4 \frac{11}{13}$$