Suppose that a graph of a system of linear equations consists of two lines that coincide. How many solutions does the system have? Explain your reasoning.

Question

The answer has to explain why the coinciding lines have infinitely many solutions.

Answer 1

Montana, let's think about it. The solution to a system of equations is the point that makes both equations true. If two lines intersect, the one point where that happens is the solution. If the lines are parallel, then there are no solutions. If they are the same line (coinciding), then any point you pick along the line will make both equations true.