Solve the following system of equations by using the method of cross multiplication:

3x + 2y + 25 = 0, 2x + y + 10 = 0

Given,

Equations :

⇒ 3x + 2y + 25 = 0

⇒ 2x + y + 10 = 0

By cross-multiplication method,

$\Rightarrow \dfrac{x}{(2) \times (10) - (1) \times (25)} = \dfrac{y}{(25) \times (2) - (10) \times (3)} = \dfrac{1}{(3) \times (1) - (2) \times (2)} \\[1em] \Rightarrow \dfrac{x}{20 - 25} = \dfrac{y}{50 - 30} = \dfrac{1}{3 - 4} \\[1em] \Rightarrow \dfrac{x}{-5} = \dfrac{y}{20} = \dfrac{1}{-1} \\[1em] \Rightarrow \dfrac{x}{-5} = \dfrac{1}{-1} \text{ and } \dfrac{y}{20} = \dfrac{1}{-1} \\[1em] \Rightarrow x = \dfrac{-5}{-1} \text{ and } y = \dfrac{20}{-1} \\[1em] \Rightarrow x = 5 \text{ and } y = -20.$

Hence, x = 5 and y = -20.