Question

{ | y-1 |+x=2
{ 2x+y=3
Решите систему уравнений, модуль - |

Answer 1

|y - 1| + x = 2
2x + y = 3

x = 2 - |y - 1|
2x + y = 3 

x = 2 - |y - 1|
2(2 - |y - 1|) + y = 3

x = 2 - |y - 1|
4 - 2|y - 1| + y = 3

1) y ≥ 1
x = 2 - (y - 1)
4 - 2(y - 1) + y = 3

x = 3 - y
4 - 2y + 2 + y = 3

x = 3 - y
6 - y = 3

x = 3 - y
y = 3

x = 0
y = 3

2) y ≤ 1
x = 2 + (y - 1)
4 + 2(y - 1) + y = 3

x = 1 + y 
4 + 2y - 2 + y = 3

x = 1 + y
2 + 3y = 3

x = 1 + y
3y = 1

x = 1 + y
y = 1/3 

x = 4/3
y = 1/3

Ответ: (0; 3), (4/3; 1/3).