<u>the correct question is</u>
The denarius was a unit of currency in ancient rome. Suppose it costs the roman government 10 denarii per day to support 4 legionaries and 4 archers. It only costs 5 denarii per day to support 2 legionaries and 2 archers. Use a system of linear equations in two variables. Can we solve for a unique cost for each soldier? 
Let
x-------> the cost to support a legionary per day
y-------> the cost to support an archer per day
we know that
4x+4y=10 ---------> equation 1
2x+2y=5 ---------> equation 2
If you multiply equation 1 by 2
2*(2x+2y)=2*5-----------> 4x+4y=10
so
equation 1 and equation 2 are the same
The system has infinite solutions-------> Is a consistent dependent system
therefore
<u>the answer is</u>
We cannot solve for a unique cost for each soldier, because there are infinite solutions. 
 
        
             
        
        
        
Answer:
The equation in the slope-intercept form will be:
y  = 1/4x - 7
Step-by-step explanation:
Given the points




We know that the slope-intercept of line equation is

where m is the slope and b is the y-intercept
substituting m = 1/4 and the point (-4, -8) to find the y-intercept 'b'
y = mx+b
-8 = 1/4(-4)+b
-8 = -1 + b
b = -8+1
b = -7
so the y-intercept = b = -7
substituting m = 1/4 and b = -7 in the slope-intercept form of line equation
y = mx+b
y  = 1/4x + (-7)
y  = 1/4x - 7
Thus, the the equation in slope-intercept form will be:
y  = 1/4x - 7
 
        
             
        
        
        
28: 1, 2, 4, 7, 14, 28
40: 1, 2, 4, 5, 8, 10, 20, 40
The common factors are 1, 2, and 4.
You can use a factor rainbow to help you find the factors (:
        
             
        
        
        
Answer:
1.8 minutes or 108 seconds 
Step-by-step explanation:
The question tells us that the larger belt moves 300 lbs in 2 mins. And this is equal to 150 lb per minute
 
The question also tells us that a smaller belt moves the same quantity of 300 lbs in 18 mins. And this is equal to an average of 16.667 lb per min.
 
Both belts will move at a rate of 166.667 lb per min.
 
So it will take them 300 / 166.667 = 1.8 min or 108 s.
Therefore, the answer is 1.8 min