Question

Решите систему уравнений { x-y=5 {x²+2xy+y²=9

Answer 1

x-y=5

x²+2xy+y²=9

(х+у)² = 9

х₁+у₁ = 3

х₂+у₂ = -3

Сложим с первым уравнением

х₁+у₁+х₁-у₁ = 3+5

2х₁ = 8

х₁ = 4, у₁ = -1

х₂+у₂+х₂-у₂ = -3+5

2х₂ = 2

х₂ = 1, у₂ = -4

Answer 2

$\left \{ {{x-y=5} \atop {x^{2}+2xy+y^{2}=9}} \right.\\\\\left \{ {{x-y=5} \atop {(x+y)^{2} =9}} \right.\\\\1)+\left \{ {{x-y=5} \atop {x+y=3}} \right.\\ -------\\\\2x=8\\\\x_{1} =4\\\\y_{1}=3-x=3-4=-1\\\\2)+\left \{ {{x-y=5} \atop {x+y=-3}} \right. \\--------\\\\2x=2\\\\x_{2}=1\\\\y_{2}=-3-x=-3-1=-4$

Ответ : (4 ; - 1) , ( 1 ; - 4)