Решите систему уравнений: { x+xy+y=11 { x-xy+y=1 нужно подробное решение! 16 пунктов за решение!

{ x+xy+y=11

{ x-xy+y=1

{x(1+y)+y=11

{x(1-y)+y=1

{x(1+y)+y=11

{x(1-y)=1-y |: 1-y не равно нулю, у не равен 1.

{x(1+y)+y=11                                             при у=1 {х+х+1=11

{x=1                                                                      {x-x+1=1

1+y+y=11                                                               {2x=10

2y=11-1                                                                 {0x=0

2y=10

y=10:2                                                                   x=5

y=5                                                    

x-любое

ответ: (1;5), (5;1)

x+xy+y=11             

+                  =>  2x+2y=12  =>   x=6-y

x-xy+y=1

x=6-y

6-y+(6-y)y+y=11

x=6-y

y=1; 5

(1; 5), (5; 1)