х+у=14
х²+у²=100
(система)

x + y = 14 -> (x+y)^2 = x^2 + 2xy + y^2 = 2xy + 100 = 14^2 = 196

2xy = 196 - 100 = 96

x^2 - 2xy - y^2 = (x - y)^2 = 100 - 96 = 4

x + y = 14

|x - y| = 2 -> x - y = +- 2

(x+y) + (x-y) = 2x = 14 +- 2 = {16, 12}, x = {8, 6}

(x+y) - (x-y) = 2y = 14 -+2 = {12,16}, y = {6,8}

Ответ: {x = 8, y = 6} U {x = 6, y = 8}