I am really impressed by your logic JonesDaBoi 
I thought I might just try to do it by conventional algebra.
$$\\Find\;\; 2C+3T\\
6C+3T=4800 \rightarrow \;2C+1T=1600 \rightarrow \;2C=1600-1T \;\;(1)\\
8C+1T=4600 \rightarrow 1T=4600-8C \;\;(2)\\
$sub $ (2)\;\; into\;\;(1)\\
2C=1600-(4600-8C)\\
2C=1600-4600+8C\\
-6C=-3000\\
C=500\\
2C=1000\\
$sub back into (1)$\\
1000=1600-1T\\
1T=600\\
3T=1800\\
2C+3T=1000+1800=2800$$
so 2 cars and 3 Trucks are $2800
you know JonesDaBoi I like your solution better. If I could give you more points I would 