Система уравнений

{Х^2-6 ХУ+9 У^2=16

Х-У=6

Х = y + 6

X^2 = y^2 + 12y + 36

y^2 + 12y + 36 - 6y (y + 6) + 9y^2 = 16

y^2 + 12y + 36 - 6y^2 - 36y + 9y^2 = 16

4y^2 - 24y + 20 = 0

4 (y^2 - 6y + 5) = 0

D = 36 - 20 = 16 = 4^2

y1 = (6 + 4) : 2 = 5

y2 = (6 - 4) : 2 = 1

X = y + 6

X1 = 5 + 6 = 11

X2 = 1 + 6 = 7

Ответ (11; 5) ; (7; 1)