To use elimination method we are going to multiply the first equation by -4 as:
(x - 2y + z)(-4) = 4(-4)
-4x + 8y - 4z = -16
Then, we can sum the equations as:
- 4x + 8y - 4z = -16
x + y + z = 2
3x + 3y + 3z = 14
0 + 12y + 0 = 0
So, we get the equation 12y = 0. It means that y is equal to 0
12y = 0
y = 0
Then, if we replace y by 0 on the initial equations, we get:
x + z = 4
x + z = 2
Since the sum of two numbers can't be 4 and 2 at the same time, the system doesn't have a solution.
Answer: the system doesn't have a solution.