What is the solution to a system of equations telling us?

Question

The number of spaces you move to get from one line to the other

The plotted points for only one of the lines or equations

The coordinates of the ordered pair(S) that satisfy both equations in the system. In other words, the values of x and y that will make equitation's true. Also, when a system of the equations is graphed, the solution will be all points of an intersection of the graphed lines.

It doesn't tell us anything. There is never a solution

Answer 1

The correct understanding of the solution to a system of equations is:

The coordinates of the ordered pair(s) that satisfy both equations in the system. In other words, the values of x and y that will make the equations true. Also, when a system of equations is graphed, the solution will be all points of intersection of the graphed lines.

This means that if you have a system of equations, the solution represents the point(s) (x, y) where the equations intersect when graphed, indicating values that make both equations true simultaneously. If the lines do intersect, there is a unique solution (one intersection point). If the lines are parallel, there is no solution, and if the lines coincide, there are infinitely many solutions.