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 lincar cquations in two variables. Can we solve for a unique cost for each soldier?

Answer 1

Given Data

Let the denarius currency have a symbol of D

let the cost of each legionary be x

and

let the cost of each archer be y

From the question, the linear equation will be

4x + 4y = D10/day -----------(1)

2x + 2y = D5/day------------(2)

Step 1

Solve the linear equations

x1 (4x + 4y = 10) --------------(3)

x2 (2x+2y= 5 )-----------------(4)

4x +4y = 10

-

4x + 4y = 10

------------------

0 0 = 0

Since both equations are the same and the variables have coefficients of the same value, we will have just zeroes and no solution, then we can see that we cannot solve for the unique cost of each soldier. Since the equation has infinitely many solutions.

The answer is NO