Answer:
the equation D ) would cause a consistent-independent system.
Step-by-step explanation:
A ) 5 x + y = 7  /*( -2 )
     10 x + 2 y = 14
     --------------------
     - 10 x - 2 y = - 14
       10 x + 2 y = 14
    ------------------------
        0 x = 0  ( Dependent system )
B ) 5 x + y = 7  / *  3 
     - 15 x - 3 y = - 6
     --------------------------
     15 x + 3 y  = 21 
     - 15 x - 3 y = - 6
   -------------------------
         0 x = 15 ( Inconsistent system )
C )   5 x + y = 7
        5 x + y = - 7  / * ( - 1 )
        ---------------------------
        5 x + y = 7
       - 5 x - y = 7
     ------------------
         0 x = 14  ( Inconsistent system )
D ) 5 x + y = 7  / * ( - 2 )
      6 x + 2 y = 7
      ------------------
       - 10 x - 2 y = - 14
         6 x   + 2 y = 7
       -----------------------
        - 4 x = - 7;     x = 7/4;   y = - 7/4
 
        
             
        
        
        
.2 (simplified from 0.20)
2/10 (simplified from 20/100)
        
                    
             
        
        
        
Answer:
Number of hot dogs sold =  56
Number of  hamburgers sold = 52
Step-by-step explanation:
Let 
Number of hot dogs sold = x
Number of  hamburgers sold = y
We can make equation from given equations:
  (Hot dogs were sold for $.50 (fifty cents), and hamburgers were sold for $1 (one dollar). The total money raised by your class was $80. )
 (Hot dogs were sold for $.50 (fifty cents), and hamburgers were sold for $1 (one dollar). The total money raised by your class was $80. )
 (Together you sold 108 hot dogs and hamburgers.)
  (Together you sold 108 hot dogs and hamburgers.)
Now we cam solve these system of equations to find value of x and y

Subtract both equations to get value of x:

We get value of x = 56
Now putting value of x in equation 2 to find value of y

So, we get y = 52
Therefore,
Number of hot dogs sold = x = 56
Number of  hamburgers sold = y = 52
 
        
             
        
        
        
Answer: (10,9) is the correct answer.