Sure, let's break down the problem step-by-step.
### Understanding the Question:
We have a system of three linear equations whose solution set forms a line. We are asked to determine the nature of this system based on the given information.
### Key Concepts:
1. Independent System: An independent system of equations has a single unique solution where all the equations intersect at one point.
2. Dependent System: A dependent system of equations has an infinite number of solutions, usually because the equations essentially define the same line or plane.
3. Consistent System: A consistent system has at least one solution.
4. Inconsistent System: An inconsistent system has no solutions because the equations describe parallel lines or planes that never intersect.
### Analysis:
- If the solution to the given system of three linear equations forms a line, this implies that there is not just a single point of intersection, but rather an infinite number of points lying on that line.
- Hence, the system cannot be independent since an independent system would have exactly one solution.
- By the nature of having an infinite number of solutions along the line, the system must be consistent (since there are solutions) and dependent (since we have more than one solution).
### Conclusion:
Given the above considerations, the system of three linear equations in question can only be dependent and consistent. Therefore, the correct answer is:
- The system can only be dependent and consistent.
This conclusion leads us to select option:
- The system can only be dependent and consistent.
