1)1/x+y = a, 1/x-y = b

{a+b = 15 |•(-3)

{3a+10b = 101

{-3a-3b = -45

{3a+10b = 101

7b = 56

b = 8

a = 15-b = 7

2)

{1/x+y = 7

{1/x-y = 8

{x+y = 1/7

{x-y = 1/8

2x = 7/56+8/56

2x = 15/56

x = 15/112

y = 16/112 - x = 1/112

Ответ: {15/112; 1/112}