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

Given equations:
1) x - y + 2z = 14
2) x - 3z = 2
3) -3x - 1 + 2z = -1

From equation 2), we can express x in terms of z:
x = 2 + 3z

Now substitute this value of x into equation 1) and equation 3):
1) (2 + 3z) - y + 2z = 14
2) -3(2 + 3z) - 1 + 2z = -1

Simplify them:
1) 5z - y = 12
2) -6 - 9z - 1 + 2z = -1
-9z + 2z - 7 = 0
-7z = 7
z = -1

Now, substitute z = -1 back into equation 2) to find x:
x - 3(-1) = 2
x + 3 = 2
x = -1

Now, substitute x = -1 and z = -1 into equation 1) to find y:
-1 - y + 2(-1) = 14
-1 - y - 2 = 14
-y - 3 = 14
-y = 17
y = -17

Therefore, the solution to the system of equations is:
x = -1
y = -17
z = -1