2.464 Решите уравнение: a) (z - 6) = 3; б) 5y - 5 = 5.

a) $$(z - 6) \div \frac{3}{7} = 3$$

$$z - 6 = 3 \cdot \frac{3}{7}$$ $$z - 6 = \frac{9}{7}$$ $$z = 6 + \frac{9}{7}$$ $$z = \frac{42 + 9}{7}$$ $$z = \frac{51}{7} = 7\frac{2}{7}$$

б) $$5\frac{1}{4}y - 5\frac{5}{6} = 5\frac{1}{4}$$ $$\frac{21}{4}y = 5\frac{1}{4} + 5\frac{5}{6}$$ $$\frac{21}{4}y = \frac{21}{4} + \frac{35}{6}$$ $$\frac{21}{4}y = \frac{21 \cdot 3 + 35 \cdot 2}{12}$$ $$\frac{21}{4}y = \frac{63 + 70}{12}$$ $$\frac{21}{4}y = \frac{133}{12}$$ $$y = \frac{133}{12} \cdot \frac{4}{21}$$ $$y = \frac{133}{3 \cdot 21} = \frac{133}{63} = 2\frac{7}{63} = 2\frac{1}{9}$$

Ответ: a) 7; б) 2