Does line shave to cross on graph to be an infinite number of solutions

Answer 1

For a system of linear equations to have an infinite number of solutions, the lines must be coincident, meaning they are the same line. Here’s a more detailed breakdown:

1. **Coincident Lines:** If two lines on a graph are identical (i.e., they lie on top of each other), every point on one line is also a point on the other line. This means there are an infinite number of solutions, as infinitely many points satisfy both equations simultaneously.

2. **Parallel Lines:** If the lines have the same slope but different y-intercepts, they are parallel and never intersect. In this case, there are no solutions since there are no points that satisfy both equations.

3. **Intersecting Lines:** If the lines have different slopes, they will intersect at exactly one point. In this case, there is exactly one solution, the point of intersection.

So, for an infinite number of solutions, the lines do not "cross" in the traditional sense (like intersecting lines). Instead, they overlap entirely, sharing all points in common. This typically means the equations of the lines are multiples of each other, representing the same geometric line on the graph.