Question

The denarius was a unit of currency in ancient rome. Suppose it costs the roman government 101010 denarii per day to support 444 legionaries and 444 archers. It only costs 555 denarii per day to support 222 legionaries and 222 archers. Use a system of linear equations in two variables. Can we solve for a unique cost for each soldier? Choose 1 answer:

Answer 1

the correct question is

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?

Let

x-------> the cost to support a legionary per day

y-------> the cost to support an archer per day

we know that

4x+4y=10 ---------> equation 1

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

If you multiply equation 1 by 2

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

so

equation 1 and equation 2 are the same

The system has infinite solutions-------> Is a consistent dependent system

therefore

the answer is

We cannot solve for a unique cost for each soldier, because there are infinite solutions.