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

The system of equations you provided is:

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

However, there seems to be a mistake in the third equation. It should probably be 2x + y - z = 2 (without the extra z).

Assuming that's the case, let's solve the system step by step:

Step 1: Subtract the first equation from the second and third equations to eliminate x:

2. • 1. gives: y + 2z = 3
3. • 1. gives: x = 1

Step 2: Substitute x = 1 into the first and second equations:

1. gives: 1 + y + z = 1, which simplifies to y + z = 0
2. gives: 1 + 2y + 3z = 4, which simplifies to 2y + 3z = 3

Step 3: Subtract the first equation from the second to eliminate y:

2. • 1. gives: y + 3z = 3, which simplifies to z = 3

Step 4: Substitute z = 3 into the first equation:

1. gives: y + 3 = 0, which simplifies to y = -3

So the solution to the system of equations is x = 1, y = -3, z = 3.