Solution of equation $\dfrac{2}{x} + \dfrac{3}{y}$ + 1 = 0 and $\dfrac{3}{x} + \dfrac{5}{y}$ + 2 = 0 is:

1. -1 and -1

2. -1 and -2

3. 1 and -1

4. none of these

Given, $\dfrac{2}{x} + \dfrac{3}{y}$ + 1 = 0 and $\dfrac{3}{x} + \dfrac{5}{y}$ + 2 = 0

Let $\dfrac{1}{x}$ be u and $\dfrac{1}{y}$ be v.

⇒ 2u + 3v + 1 = 0 ……………….(1)

⇒ 3u + 5v + 2 = 0 ……………….(2)

Multiplying eq. (1) by 3, we get,

⇒ 6u + 9v + 3 = 0 …………….(3)

Multiplying eq. (2) by 2, we get,

⇒ 6u + 10v + 4 = 0 …………….(4)

Subtracting eq. (3) from (4) we get,

⇒ 6u + 10v + 4 - (6u + 9v + 3) = 0 - 0

⇒ 6u + 10v + 4 - 6u - 9v - 3 = 0

⇒ v + 1 = 0

⇒ v = -1

⇒ $\dfrac{1}{y}$ = -1

⇒ y = -1

Substituting value of v in eq. (2) we get

⇒ 3u + 5(-1) + 2 = 0

⇒ 3u - 5 + 2 = 0

⇒ 3u - 3 = 0

⇒ 3u = 3

⇒ u = $\dfrac{3}{3}$

⇒ u = 1

⇒ $\dfrac{1}{x}$ = 1

⇒ x = 1

∴ x = 1 and y = -1

Hence, option 3 is the correct option.