{-2x + 3y -z =4 (1)
{ x + y + z = -7 (2)
{4x - 3y - z = 6 (3)
(1) + (3)
- 2х + 3у -z + 4x -3y -z =4+6
2x - 2z = 10
2(x-z) = 10
x-z = 5
x= 5+z
(1)*2 + (3)
-4x +6y -2z +4x - 3y -z = 8+6
3y -3z = 14
3(y-z) = 14
y-z = 14/3
y= 14/3 + z
y= 4 2/3 +z
подставим значения х и у в уравнение (2):
5+z + 4 2/3 + z + z = -7
3z + 9 2/3 = -7
3z = -7 - 9 2/3
3z = - 16 2/3
z = - 16 2/3 : 3 = - 50/3 * 1/3 = -50/9
z= - 5 5/9
x= 5 + (-5 5/9)
x= - 5/9
y= 4 2/3 + ( - 5 5/9)= 4 6/9 - 5 5/9 = 42/9 - 50/9
y= - 8/9
Ответ: ( -5/9 ; - 8/9 ; - 5 5/9)