<PRE><B>Question 26100</B>
3 equations and 3 unknowns. Take 2 equations at a time and try to eliminate 1 common variable

3A + B + 4C = 34        (1)
2A + 2B + C = 26        (2)
A + 2B + 3C = 23        (3)

Subtracting (3) fm (2)
A - 2C = 3              (4)

Multiplying (1) with 2
6A+2B+8C = 68                 (5)
Subtracting (2) fm (5)
4A+7C = 42     (6)

Multiplying (4) with 4
4A-8C = 12            (7)

Subtracting (7) fm (6)
15C = 30
Dividing by 15 throughout
C = 2

Putting this back in (4)
A - 2(2) = 3
Adding 4 on both sides 
A = 7
Putting this back in any of (1),(3),(2)
B = 5</PRE>