Решите систему.

-2 х+3 у-z=4

x+y+z=-7

4x-3y-z=6

{-2x + 3y - z = 4 (1)

{ x + y + z = - 7 (2)

{4x - 3y - z = 6 (3)

(1) + (3)

- 2 х + 3 у - 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)