Systems of equations can be classified by the number of solutions. If a system has at least one solution, it is said to be consistent .

Answer 1

If a system has no solutions, it is said to be inconsistent.

There are three possible scenarios for a system of equations:

1. Consistent system with one solution: In this case, the system of equations has a unique solution that satisfies both equations. The lines representing the equations will intersect at a single point.

2. Consistent system with infinite solutions: In this case, the system of equations has an infinite number of solutions, and the equations represent the same line or lines that overlap. The lines representing the equations will coincide.

3. Inconsistent system with no solutions: In this case, there is no solution that satisfies both equations. The lines representing the equations are parallel and will never intersect.

The number of solutions that a system of equations has can provide important information about the relationship between the equations and the variables involved.