Explain what it means to graphically for a system to have no solution

Answer 1

When a system of equations is graphically shown to have no solution, it means that the lines representing each equation do not intersect at any point on the graph. This signifies that there is no common solution that satisfies both equations simultaneously. In other words, the two lines representing the equations are parallel and never intersect, indicating that there is no combination of values for the variables that can satisfy both equations at the same time. This situation indicates that the system is inconsistent and has no solution.