Question

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. Use a system of linear equations in two variables. Can we solve for a unique cost for each soldier?

Answer 1

The system cannot be solved by a unique cost for each soldier, because has infinite solutions

Explanation:

Let

x-------> the cost of a legionary per day

y-------> the cost of an archer per day

we know that

`4x+4y=10` ------> equation A

`2x+2y=5` ------> equation B

Multiply equation B by
`2` both sides

`2(2x+2y)=2*5` ------->
`4x+4y=10`

so

equation A and equation B is the same equation

therefore

This is a consistent dependent system

The system has infinite solutions