If a pair of linear equation is consistent, then the lines will be:a)Parallelb)Always coincidentc)Intersecting or coincidentd)Always intersecting

To determine the correct answer, let's first understand what it means for a pair of linear equations to be consistent.

A system of linear equations is said to be consistent if there is at least one solution. This implies that the lines represented by the equations either intersect at a single point (unique solution) or are coincident (infinite solutions).

Now, let's analyze the options:

a) Parallel: If the lines are parallel, they will never intersect, meaning there is no solution. This would make the system inconsistent. So, this option is incorrect.

b) Always coincident: Coincident lines have infinite solutions, which means the system is consistent. However, the system may not always have coincident lines unless specifically given. This is not always true for consistent systems. So, this option is not correct.

c) Intersecting or coincident: This is the correct answer. For a consistent system, the lines will either intersect at a unique point (one solution) or coincide (infinite solutions).

d) Always intersecting: This option suggests that the lines always intersect, but it doesn't account for the possibility of coincident lines. The system could have infinite solutions, which means the lines coincide. Hence, this option is not fully accurate.

Therefore, the correct answer is c) Intersecting or coincident.