Решите систему уравнений (x+y) (x-y) = 0 и 2x-y=1

Решение

Решите систему уравнений

(x+y) (x-y) = 0

2x-y=1

x² - y² = 0

y = 2x - 1

y = 2x - 1

x² - (2x - 1) ² = 0

x² - 4x² + 4x - 1 = 0

- 3x² + 4x - 1 = 0

3x² - 4x + 1 = 0

D = 16 - 4*3*1 = 4

x1 = (4 - 2) / 6

x1 = 1/3

x2 = (4 + 2) / 6

x2 = 1

x1 = 1/3

y1 = 2 * (1/3) - 1

y1 = - 1/3

x2 = 1

y2 = 2*1 - 1

y2 = 1

Ответ: (1/3; - 1/3) ; (1; 1)