How do you solve this system using any algebraic method

4x+2y-z=4
2x-3y+2z=4
x+y-z=-1

4x + 2y - z = 4 . . . . . [1]
2x - 3y + 2z = 4 . . . . [2]
x + y - z = 1 . . . . . . . [3]

From [1] -----> z = 4x + 2y - 4 . . . [4]
From [3] -----> z = x + y + 1. . . . . [5]

From [4] and [5]
4x + 2y - 4 = x + y + 1
2y - y = x + 1 - 4x + 4
y = -3x + 5 . . . . . . . . . . . . . . . . . [6]

Using this value of y in [5] we get
z = x + (-3x + 5) + 1
z = -2x + 6 . . . . . . . . . . . . . . . . . [7]

Using values of y (from [6]) and y (from [7]) in equation [2], we get

2x - 3(-3x+5) + 2(-2x+6) = 4
2x + 9x - 15 - 4x + 12 = 4
7x - 3 = 4
7x = 7
x = 1

y = -3x + 5 = -3 + 5 = 2

z = -2x + 6 = -2 + 6 = 4

x = 1
y = 2
z = 4

X=1
Y=2
Z=4