Question

if two equations represent the same line, the system has solutions.

Explanation:

Identify the system characteristics

The question asks about the number of solutions when two equations in a system represent the same line. We use the System of Equations Definition to understand that a system's solution is any point that satisfies all equations in the system.

Analyze the graphical representation

Using the Graphical Solution of Systems, the solutions to a system of linear equations correspond to the intersection points of their graphs. Since both equations represent the exact same line, the two lines lie directly on top of each other (they are coincident).

Determine the number of solutions

Because the lines are identical, every single point on the line is a point of intersection. A line contains an infinite number of points. Therefore, the system has infinitely many solutions.

Answer:

If two equations represent the same line, the system has <blank>infinitely many</blank> solutions.