Question

решить систему уравнений:
А) x + y = 9 ,
(x-1)(y+1)=0;
Б) x-y=8,
(x+2)(y-4)=0;

Answer 1

Ответ:

A) x + y = 9,

(x-1)(y+1) = 0
x - 1 = 0 --> x = 1

y + 1 = 0 --> y = -1
x + y = 1 + (-1) = 0 ≠ 9




B) x - y = 8,

(x+2)(y-4) = 0
x + 2 = 0 --> x = -2

y - 4 = 0 --> y = 4
x - y = -2 - 4 = -6 ≠ 8

Answer 2

а)

{ x + y = 9

{ (x - 1)(y + 1) = 0

{ x = 9 - y

{ (9 - y - 1)(y + 1) = 0

(8 - y)(y + 1) = 0

8y + 8 - y² - y = 0

7y + 8 - y² = 0

y² - 7y - 8 = 0

D = (-7)² - 4 * (-8) = 49 + 32 = 81 = 9²

y₁ = (7 - 9)/2 = -2/2 = -1   ⇒  x₁ = 9 + 1 = 10

y₂ = (7 + 9)/2 = 16/2 = 8  ⇒  x₂ = 9 - 8 = 1

Ответ: (10; -1), (1; 8)

б)

{ x - y = 8

{ (x + 2)(y - 4) = 0

{ x = 8 + y

{ (8 + y + 2)(y - 4) = 0

(10 + y)(y - 4) = 0

10y - 40 + y² - 4y = 0

y² + 6y - 40 = 0

D = 6² - 4 * (-40) = 36 + 160 = 196 = 14²

y₁ = (-6 - 14)/2 = -20/2 = -10  ⇒  x₁ = 8 - 10 = -2

y₂ = (-6 + 14)/2 = 8/2 = 4       ⇒  x₂ = 8 + 4 = 12

Ответ: (-2; -10), (12; 4)