When you graph a system of linear equations why does the intersection of two lines repesent the solution of the system?

The intersection of two lines in a graph of a system of linear equations represents the solution because it indicates the point where both equations are true simultaneously. This point has coordinates that satisfy both equations, meaning that the values of the variables at this point fulfill the conditions set by each equation. Consequently, the intersection reflects a unique solution for the system, representing the values of the variables that solve both equations. If the lines do not intersect, it indicates that there is no common solution.