Final answer:
The given system of equations has an infinite number of solutions because the two equations represent the same line, therefore the system is consistent and dependent.
Step-by-step explanation:
To determine the number of solutions of the given system of equations:
5x - 2y = -17
20x + 4y = -56
First, we observe that the second equation is exactly four times the first one. This means that the two equations are actually the same when the second is reduced, indicating that they are dependent equations. As such, every solution to the first equation is also a solution to the second equation, meaning that there is an infinite number of solutions. This system is consistent and dependent.