You need to solve
You you know how to find this inverse?
You can use this Matrix calculator
Assuming you know simple matrix operations like mulitplication and finding determinants,
To solve the system consider cramer's Method.
Cramer's rule - Wikipedia, the free encyclopedia
If you don't know these elementary ideas I suggest this problem should be solved using subtitution and elimination.
(1) X + Y + Z = 18
(2) X - Y - Z = 12
(3) 3X - 2Y + 4Z = 4
Here's my simplistic and basic method
Rearranging (1) to isolate X
Substituting into (2)
Rearranging this gives:
Taking out (and then dividing through by) a common factor of 2 gives
Substituting this into equation 1 gives
Substituting that into all equations leaves:
Which can then be solved easily simultaneously to give
Then substituting this back into the above equations will give