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

Question 5

Step 1: Understand the equations.

The equation \(x = a\) is a vertical line passing through all points where the \(x\)-coordinate is always \(a\).

The equation \(y = b\) is a horizontal line passing through all points where the \(y\)-coordinate is always \(b\).

Step 2: Check their intersection.

The vertical line \(x = a\) and the horizontal line \(y = b\) meet at a single point.

This point has coordinates where \(x = a\) and \(y = b\), i.e., the point \((a, b)\).

Step 3: Verify the options.

(A) Parallel → Incorrect, since they cross each other.

(B) Intersecting at \((b,a)\) → Incorrect, order of coordinates is wrong.

(C) Coincident → Incorrect, because the lines are distinct and not overlapping.

(D) Intersecting at \((a,b)\) → Correct, since that is the only common point.

Final Answer: Option (D), the lines intersect at \((a,b)\).