Question

1. If the two lines intersect at a single point, then there is ______ solution for the system.

2. If the two lines are parallel to each other (not touching), then there is ______ solution for the system.
3. If one line is on top of the other line (coinciding lines), then there are ______ solutions for the system.
4. The places where the lines intersect represent ______ of the system of linear equations.

Answer 1

The intersection of two lines on a graph indicates the number of solutions for the system: one unique solution if they intersect at one point, no solution if they are parallel, and infinitely many solutions if they coincide.

Step-by-step explanation:

When dealing with systems of linear equations and their graphical representations, the intersection of two lines on a graph can result in different scenarios. These scenarios are tied to the number of solutions the system has.

• If the two lines intersect at a single point, then there is one unique solution for the system.
• If the two lines are parallel to each other and do not intersect, then there is no solution for the system, as they have no points in common.
• If one line is exactly on top of the other line (coinciding lines), then there are infinitely many solutions for the system, as every point on one line is also a point on the other line.
• The places where the lines intersect represent the solutions of the system of linear equations.