To determine the number of solutions for a system of linear equations, we need to analyze the relationship between the graphs of the equations. Let's examine the given options:
Option A: There is exactly one solution.
This would be true if the graphs of the linear equations intersect at a single point. However, if the graphs are the same line, they coincide at every point on the line, so this option is incorrect.
Option B: There is no solution.
This would be true if the graphs of the linear equations are parallel lines that never intersect. However, if the graphs are the same line, they overlap completely, and thus this option is incorrect.
Option C: There are infinitely many solutions.
If the graphs of the linear equations are the same line, every point on one line is also a point on the other line. This means that there are an infinite number of points that satisfy both equations. Therefore, this option is correct.
Option D: The lines in a system cannot graph as the same line.
This is not true. Linear equations can have the same graph if they are identical in terms of slope and intercept or are multiples of each other. Therefore, this option is incorrect.
Since the graphs of the linear equations in the system are the same line,
Option C: There are infinitely many solutions is the correct answer.
