Solution of equations 15x + 6y = 27 and 6x + 15y = 36 is :

1. x = 1, y = -2

2. x = -1, y = 2

3. x = 1, y = 2

4. x = -1, y = -2

Given, equations can be written as :

⇒ 15x + 6y - 27 = 0 …….(1)

⇒ 6x + 15y - 36 = 0 ……..(2)

By cross-multiplication method :

$\Rightarrow \dfrac{x}{6 \times (-36) - 15 \times (-27)} = \dfrac{y}{(-27) \times 6 - (-36) \times 15} = \dfrac{1}{15 \times 15 - 6 \times 6} \\[1em] \Rightarrow \dfrac{x}{-216 + 405} = \dfrac{y}{-162 - (-540)} = \dfrac{1}{225 - 36} \\[1em] \Rightarrow \dfrac{x}{189} = \dfrac{y}{-162 + 540} = \dfrac{1}{189}\\[1em] \Rightarrow \dfrac{x}{189} = \dfrac{y}{378} = \dfrac{1}{189}\\[1em] \Rightarrow \dfrac{x}{189} = \dfrac{1}{189} \text{ and } \dfrac{y}{378} = \dfrac{1}{189} \\[1em] \Rightarrow x = \dfrac{189}{189} \text{ and } y = \dfrac{378}{189} \\[1em] \Rightarrow x = 1 \text{ and } y = 2.$

Hence, Option 3 is the correct option.