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:

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

Step-by-step 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.

Answer 2

Answer: No solutions

Step-by-step explanation: