The denarius was a unit of currency in ancient Rome. Suppose it costs the Roman government 10 denarii per day to support 4 legionaries and 4 archers. It only costs 5 denarii per day to support 2 legionaries and 2 archers.
Can we solve for a unique cost for each soldier?
No, you can't
4 L + 4 A = 10 is basically the same equation as
2 L + 2 A = 5 (just divided by 2)