Найдем корень уравнения:
$$\frac{5}{7}y + \frac{2}{3}y - 4 = \frac{1}{7}$$
$$\frac{15}{21}y + \frac{14}{21}y = \frac{1}{7} + 4$$
$$\frac{29}{21}y = \frac{1}{7} + \frac{28}{7}$$
$$\frac{29}{21}y = \frac{29}{7}$$
$$y = \frac{29}{7} : \frac{29}{21}$$
$$y = \frac{29}{7} \cdot \frac{21}{29} = 3$$
Ответ: 3