Solve the system: x + y + z = 6, 2x – y + z = 3, x + y – z = 0Question 6Select one:a.(0, 0, 6)b.(3, 2, 1)c.(0, 0, 1)d.(1, 2, 3)e.None of these

To solve the system of equations, we can use the method of substitution or elimination. Here, we will use the elimination method.

The system of equations is:

1. x + y + z = 6
2. 2x - y + z = 3
3. x + y - z = 0

First, let's subtract the third equation from the first to eliminate y and z:

(x + y + z) - (x + y - z) = 6 - 0 This simplifies to: 2z = 6 So, z = 6 / 2 = 3

Now, substitute z = 3 into the first and third equations:

1. x + y + 3 = 6 So, x + y = 6 - 3 = 3

2. x + y - 3 = 0 So, x + y = 0 + 3 = 3

Both simplified equations are the same, so they give us no new information.

Now, substitute z = 3 into the second equation:

2x - y + 3 = 3 So, 2x - y = 3 - 3 = 0 So, 2x = y

Substitute y = 2x into the equation x + y = 3:

x + 2x = 3 So, 3x = 3 So, x = 3 / 3 = 1

Substitute x = 1 into the equation 2x = y:

2*1 = y So, y = 2

So, the solution to the system of equations is x = 1, y = 2, z = 3. Therefore, the correct answer is d. (1, 2, 3).