{ x + y = -8
{ x^2 + y^2 + 6x + 2y = 0
Преобразуем 2 уравнение
{ x + y = -8
{ (x^2 + 6x + 9) - 9 + (y^2 + 2y + 1) - 1 = 0
Сворачиваем полные квадраты
{ y = -8 - x
{ (x + 3)^2 + (y + 1)^2 - 10 = 0
Подстановка
(x + 3)^2 + (-8 - x + 1)^2 - 10 = 0
(x + 3)^2 + (-7 - x)^2 - 10 = 0
x^2 + 6x + 9 + x^2 + 14x + 49 - 10 = 0
2x^2 + 20x + 48 = 0
x^2 + 10x + 24 = 0
(x + 4)(x + 6) = 0
x1 = -6; y1 = -8 + 6 = -2
x2 = -4; y2 = -8 + 4 = -4