What is the solution to the system of equations? - 7x-2y+z=-2

6x-y-z=-18

5x+4y-z=18

x = - 1, y = 7, z = 5.

Step-by-step explanation:

-7x - 2y + z = - 2 ... (1)

6x - y - z = - 18 ... (2)

5x + 4y - z = 18 ... (3)

Subtract equations (2) - (3):

x - 5y = - 36 ... (4)

Add equations (1) and (2):

-x - 3y = - 20 ... (5)

Adding (4) and (5):

-8y = - 56

y = 7.

Substitute y = 7 into equation 4:

x - 5 (7) = - 36

x - 35 = - 36

x = - 1.

Substitute x = - 1 and y = 7 in equation (1):

-7 (-1) - 2 (7) + z = - 2

7 - 14 + z = - 2

z = - 2 - 7 + 14

z = 5.