Final answer:
Equation 4, which states 'q + d + n = 7.25', is the equation that does not belong to the system as it incorrectly equates the total number of coins to the total value in dollars instead of the correct whole number count of coins.
Step-by-step explanation:
The student's question pertains to determining which equation does not belong to a system of equations that describes the amount and value of coins in a change machine. To answer this, we must understand that we are dealing with a word problem involving linear equations that represent quantities and total values of nickels (n), dimes (d), and quarters (q).
Equation 1 (d = 5n) suggests that there are 5 times as many nickels as dimes. Equation 2 (q + d + n = 75) represents the total number of coins. Equation 3 (0.25q + 0.10d + 0.05n = 7.25) corresponds to the total value of the coins in dollars. The incorrect equation is Equation 4 (q + d + n = 7.25), as it incorrectly implies the total number of coins is equal to the total value in dollars, which is not possible with the denominations given. The correct representation for the total number of coins is in whole numbers, not dollars.