NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 3: Pair of Linear Equations in Two Variables - Exercise 3.1

Question 3

Step 1: A system of linear equations is called consistent if it has at least one solution.

Step 2: For two lines in a plane, there are three possibilities:

• The lines intersect at a single point ⇒ one solution.
• The lines are coincident ⇒ infinitely many solutions.
• The lines are parallel and distinct ⇒ no solution.

Step 3: Since consistency means the equations have one or more solutions, the possible cases are:

• Lines intersecting at one point, or

• Lines coincident (overlapping).

Therefore: If a pair of linear equations is consistent, the lines will be intersecting or coincident.