Solve the system: x + y + z = 6, 2x – y + z = 3, x + y – z = 0

Sure, let's solve this system of equations step by step.

1. First, let's take the first and third equations:

   x + y + z = 6 x + y - z = 0

   Subtract the third equation from the first to eliminate y and z:

   (x + y + z) - (x + y - z) = 6 - 0 2z = 6 z = 3

2. Now, substitute z = 3 into the first and second equations:

   x + y + 3 = 6 2x - y + 3 = 3

   Simplify these equations to:

   x + y = 3 2x - y = 0

3. Add these two equations together:

   (x + y) + (2x - y) = 3 + 0 3x = 3 x = 1

4. Substitute x = 1 into the equation x + y = 3:

   1 + y = 3 y = 2

So, the solution to the system of equations is x = 1, y = 2, z = 3.