The denarius was a unit of currency in ancient Rome. Suppose it costs the Roman government 1 0 1010 denarius per day to support 3 33 legionaries and 3.33 archers. It only costs 3.33 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?

Question

Mathematics

Jude Hahn

6 April, 13:30

The denarius was a unit of currency in ancient Rome. Suppose it costs the Roman government 1 0 1010 denarius per day to support 3 33 legionaries and 3.33 archers. It only costs 3.33 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?

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Brent · Answer 1

assuming you copied and pasted this from khan academy and the original numbers are 10, 3, 3 and 3, make two equations:

x+y=3 and 3x+3y=10

x+y=3 - > solve for y - > y=-x+3

plug into 3x+3y=10

3x+3 (-x+3) = 10

3x-3x+9=10 - > the 3x's cancel out

9=10

however 9 does not equal 10 and therefore, there is no solution