Question

if the lines in a system of linear equations are parallel, what is the system called? enter the number that corresponds to the correct option:
1 - consistent system of equations
2 - dependent system of equations
3 - inconsistent system of equations
4 - independent system of equations
(1 point)

Explanation:

To determine the type of system of linear equations with parallel lines, we recall the definitions:

• A consistent system has at least one solution (intersecting or coinciding lines).
• A dependent system has infinitely many solutions (coinciding lines).
• An inconsistent system has no solutions (parallel lines, as they never intersect).
• An independent system is a consistent system with a unique solution (intersecting lines).

Since parallel lines never intersect, the system has no solutions, so it is an inconsistent system. The option corresponding to this is 3.

Answer:

3 - inconsistent system of equations