Question

If a pair of linear equations is consistent, then the lines will be __________

• A. parallel
• B. always coincident
• C. intersecting or coincident
• D. always intersecting

Answer 1

The correct option is C

intersecting or coincident

Explanation for the correct answer:

1. For a pair of linear equations to be consistent, the system should have at least one unique solution or infinitely many solutions.
2. When two lines intersect each other at one point, we obtain a unique solution.
3. When two lines are coincident, every point of the two lines is identical. This also implies that the line intersects at infinitely many points resulting in infinitely many solutions.
4. Thus, the only possible way for linear equations to be consistent is when the lines represented by the pair of linear equations are either intersecting or coincident.

Hence , option$\left(C\right)$ is the correct answer, as, if a pair of linear equations is consistent, then the lines will be intersecting or coincident.