If a graph of a system of two equations shows two lines that coincide on a coordinate plane, how many solutions does the system have?

When two lines coincide on a coordinate plane, it means that they are exactly the same line. In this case, every point on the line is a solution to both equations. Therefore, the system of equations has an infinite number of solutions.

This occurs because for any x-value you choose, there is a corresponding y-value that satisfies both equations. Since the two lines are not just intersecting at one point but are instead identical, they share all their points. Thus, we conclude that the system has an infinite number of solutions.

More Related Questions