The denarius was a unit of currency in ancient Rome. Suppose it costs the Roman government 101010 denarius per day to support 333 legionaries and 333 archers. It only costs 333 denarius per day to support one legionary and one archer. Use a system of linear equations in two variables.

Complete 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?

No unique solution

Step-by-step explanation:

Given that:

Cost of supporting 3 legion aries and 3 archers = 10 denarius daily

Cost of supporting one legionary and one archer = 3 denarius

Let:

Legionaries = l ; archers = a

Equation for the first sentence :

3l + 3a = 10 - - - (1)

Second sentence :

l + a = 3 - - - - - (2)

From (2)

l = 3 - a

Substituting l = 3 - a into (1)

3(3 - a) + 3a = 10

9 - 3a + 3a = 10

9 - 0 = 10

The variable cancels out, Hence, ( there is no unique solution to find the cost of each soldier)

step-by-step explanation:

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given   that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency   kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule   states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.