lets say
a+b+3c=12 (1)
2a+b+3c=14 (2)
a-b+4c=13 (3)
step 1
equation (1)-equation (3)
u will get
c=1+2b (4)
step 2
equation (1) multiply by 2
u will get: 2a+2b+6c=24 (5)
thus:
equation (5) -equation (2) and u will get;
b=10-3c
substitute b=10-3c into equation (4) and u will get the value of c
since one variables is known then it will easy to determine others