Assertion (A): Solving $\sqrt{2}x - \sqrt{3}y$ = 0, $\sqrt{3}x + \sqrt{2}y$ = 5 yields x = $\sqrt{3}$, y = $\sqrt{2}$.

Reason (R): We can use cross-multiplication method to solve a pair of linear equations.

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).

We can use cross-multiplication method to solve a pair of linear equations.

∴ Reason (R) is true.

Given, equations can be written as :

$\sqrt{2}x - \sqrt{3}y - 0$ = 0 ……………..(1)

$\sqrt{3}x + \sqrt{2}y$ - 5 = 0…………….(2)

By cross multiplication method,

$\therefore \dfrac{x}{-\sqrt{3} \times (-5) - \sqrt{2} \times 0} = \dfrac{y}{0 \times \sqrt{3} - (-5) \times \sqrt{2}} = \dfrac{1}{\sqrt{2} \times \sqrt{2} - \sqrt{3} \times (-\sqrt{3})}\\[1em] \Rightarrow \dfrac{x}{5\sqrt{3} - 0} = \dfrac{y}{0 + 5 \sqrt{2}} = \dfrac{1}{2 + 3}\\[1em] \Rightarrow \dfrac{x}{5\sqrt{3}} = \dfrac{y}{5 \sqrt{2}} = \dfrac{1}{5}\\[1em] \Rightarrow \dfrac{x}{5\sqrt{3}} = \dfrac{1}{5} \text{ and } \dfrac{y}{5 \sqrt{2}} = \dfrac{1}{5} \\[1em] \Rightarrow x = \dfrac{5\sqrt{3}}{5} \text{ and } y = \dfrac{5\sqrt{2}}{5}\\[1em] \Rightarrow x = \sqrt{3} \text{ and } y = \sqrt{2}.$

So, the solution are x = $\sqrt{3}$, y = $\sqrt{2}$

∴ Assertion (A) is true.

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

Hence, option 3 is the correct option.