Assertion (A): A solution of x - y = 1, 2x + y = $\dfrac{7}{2}$ is x = $\dfrac{3}{2}$, y = $\dfrac{1}{2}$.

Reason (R): One of the methods of solving a pair of linear equations is elimination method.

1. Assertion (A) is true, Reason (R) is false.

2. Assertion (A) is false, Reason (R) is true.

3. Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).

4. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).

One of the methods of solving a pair of linear equations is elimination method.

∴ Reason (R) is true.

Given, x - y = 1 ……………..(1)

2x + y = $\dfrac{7}{2}$ ………………(2)

Adding equation (1) and (2) we get

$\Rightarrow (x - y) + (2x + y) = 1 + \dfrac{7}{2}\\[1em] \Rightarrow x - y + 2x + y = \dfrac{2}{2} + \dfrac{7}{2}\\[1em] \Rightarrow 3x = \dfrac{9}{2}\\[1em] \Rightarrow x = \dfrac{9}{2 \times 3}\\[1em] \Rightarrow x = \dfrac{3}{2}$

Substituting the value of x in equation (1), we get :

⇒ x - y = 1

$\Rightarrow \dfrac{3}{2} - y = 1\\[1em] \Rightarrow \dfrac{3}{2} - 1 = y\\[1em] \Rightarrow \dfrac{3 - 2}{2} = y\\[1em] \Rightarrow y = \dfrac{1}{2}.$

So, x = $\dfrac{3}{2}$, y = $\dfrac{1}{2}$

∴ Assertion (A) is true.

∴ Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason (or explanation) for Assertion (A).

Hence, option 3 is the correct option.