Question

The denarius was a unit of currency in ancient Rome. Suppose it costs the Roman government 10 denarius per day to support 3 legionaries and 3archers. It only costs 3 denarius per day to support one legionary and one archer. Use a system of linear equations in two variables. Can we solve for a unique cost for each soldier?

Answer 1

Answer: No solutions

Explanation:

Answer 2

We can not solve for a unique cost for each soldier.

Explanation:

Let x be the daily cost for legionaries and y be the daily cost for archers.

Upon using our given information we will get a system of linear equations as:

`3x+3y=10...(1)`

`x+y=3...(2)`

Now we will solve for x from our 2nd equation,

`x = 3-y`

Now we will substitute this value in our 1st equation.

`3(3-y)+3y=10`

`9-3y+3y=10`

We can see that -3y cancels out with 3y and 9 is not equal to 10. So this is an unsolvable system. Therefore, we can not find a unique cost for each soldier.