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Andru [333]
3 years ago
6

The denarius was a unit of currency in ancient Rome. Suppose it costs the Roman government 10 denarii per day to support 4 legio

naries 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?
Mathematics
1 answer:
aleksandrvk [35]3 years ago
6 0

Answer:

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

Step-by-step 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

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