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?

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:

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

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

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.

it's equivalent, so we can say that its equal.

let's call the denominator x and the numerador is 18 less then denominator, x - 18.

multiply

2.x = 5.(x - 18)

2x = 5x - 90

90 = 5x - 2x

90 = 3x

x = 90/3

x = 30

so: