Solve the system by substitution method

3x+2y+z=-2

-x-y-2z=2

2y+z=-1

First take the first equation

3x + 2y + z = - 2

then subtract z

3x + 2y + z - z = - 2 - z

simplify

3x + 2y = - 2 - z

add 2

3x + 2y + 2 = - 2 - z + 2

simplify

3x + 2y + 2 = - z

divide by - 1

-3x - 2y - 2 = z

plug z into last equation

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

simplify

-3x - 2 = - 1

add 2

-3x = 1

divide by - 3

x = - 1/3

plug x and z into second equation

- (-1/3) - y - 2 (-3 (-1/3) - 2y - 2) = 2

simplify

1/3 - y - 2 (1 - 2y - 2) = 2

distribute

1/3 - y - 2 + 4y + 4 = 2

combine like terms

2 1/3 + 3y = 2

subtract 2 1/3

3y = - 1/3

divide by 3

y = - 1/9

plug in x and y into second equation

- (-1/3) - (-1/9) - 2z = 2

simplify

1/3 + 1/9 - 2z = 2

add

4/9 - 2z = 2

subtract

-2z = 14/9

divide

z = - 7/9

answer:

x = - 1/3

y = - 1/9

z = - 7/9