2. Решите уравнение: 1) \(\frac{5}{7}(5,6 - 2,1y) = 2,4(\frac{5}{8} - \frac{2}{3}y)\) 2) \(7,6 : x = 2\frac{1}{9} : 2\frac{4}{9}\)

Решение:

1. Уравнение 1:
   \(\frac{5}{7}(5,6 - 2,1y) = 2,4(\frac{5}{8} - \frac{2}{3}y)\)
   \(\frac{5}{7}\) * \(5,6\) - \(\frac{5}{7}\) * \(2,1y\) = \(2,4\) * \(\frac{5}{8}\) - \(2,4\) * \(\frac{2}{3}y\)
   \(4 - \frac{10,5}{7}y\) = \(1,5 - \frac{4,8}{3}y\)
   \(4 - 1,5y\) = \(1,5 - 1,6y\)
   \(-1,5y + 1,6y\) = \(1,5 - 4\)
   \(0,1y\) = \(-2,5\)
   \(y\) = \(\frac{-2,5}{0,1}\)
   \(y\) = \(-25\)
   
2. Уравнение 2:
   \(7,6 : x = 2\frac{1}{9} : 2\frac{4}{9}\)
   \(7,6 : x = \frac{19}{9} : \frac{22}{9}\)
   \(7,6 : x = \frac{19}{9} \times \frac{9}{22}\)
   \(7,6 : x = \frac{19}{22}\)
   \(x\) = \(7,6 : \frac{19}{22}\)
   \(x\) = \(\frac{76}{10} \times \frac{22}{19}\)
   \(x\) = \(\frac{38}{5} \times \frac{22}{19}\)
   \(x\) = \(\frac{2 \times 19}{5} \times \frac{22}{19}\)
   \(x\) = \(\frac{2 \times 22}{5}\)
   \(x\) = \(\frac{44}{5}\)
   \(x\) = \(8,8\)

Ответ: 1) y = -25; 2) x = 8,8.