Solve the system by substitution method3x+2y+z=-2-x-y-2z=22y+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

x = -1/3
y = -1/9
z = -7/9

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