Уравнения: 1) x + 2 3/13 + 7 1/2 = 4 5/30 2) 8 7/18 - 1 11/15 + y = 3 4/15 + 2 3/5

Решение:

1) Решаем первое уравнение:

1. \( x + \frac{2\cdot3+13}{13} + \frac{7\cdot2+1}{2} = \frac{4\cdot30+5}{30} \)
2. \( x + \frac{19}{13} + \frac{15}{2} = \frac{125}{30} \)
3. \( x + \frac{19}{13} + \frac{15}{2} = \frac{25}{6} \)
4. \( x = \frac{25}{6} - \frac{19}{13} - \frac{15}{2} \)
5. \( x = \frac{25\cdot13 - 19\cdot6 - 15\cdot39}{78} \)
6. \( x = \frac{325 - 114 - 585}{78} = \frac{-374}{78} = -\frac{187}{39} \)

2) Решаем второе уравнение:

1. \( \frac{8\cdot18+7}{18} - \frac{1\cdot15+11}{15} + y = \frac{3\cdot15+4}{15} + \frac{2\cdot5+3}{5} \)
2. \( \frac{151}{18} - \frac{26}{15} + y = \frac{49}{15} + \frac{13}{5} \)
3. \( y = \frac{49}{15} + \frac{13}{5} - \frac{151}{18} + \frac{26}{15} \)
4. \( y = \frac{49+26}{15} + \frac{13}{5} - \frac{151}{18} \)
5. \( y = \frac{75}{15} + \frac{13}{5} - \frac{151}{18} \)
6. \( y = 5 + \frac{13}{5} - \frac{151}{18} \)
7. \( y = \frac{450 + 234 - 755}{90} = \frac{-71}{90} \)

Ответ: 1) x = -\(\frac{187}{39}\); 2) y = -\(\frac{71}{90}\).