The given system of equations is

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

x-y-z=-4 (2)

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

Add (1) and (2) to get 3x-4y=-2 (4)

and

Add (1) and (3) to get-x-y= 3 (5)

Solving (5) for x, x= -3-y. Substitute for x in (4) to get

3(-3-y) -4y=-2

-9-3y-4y=-2

-7y= 7

y=-1

Hence x= -3-y

= -3+1 = -2

Substitute for x and y in (2) to get

(-2) –(-1)-z=-4

-2 +1-z=-4

z=3

The required solution is x=-2; y=-1 and z=3

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