Solve, using cross-multiplication :

5x + 4y + 14 = 0

3x = -10 - 4y

Given, equations :

⇒ 5x + 4y + 14 = 0 and 3x = -10 - 4y

⇒ 5x + 4y + 14 = 0 ……….(1)

⇒ 3x + 4y + 10 = 0 ……….(2)

By cross-multiplication method :

$\Rightarrow \dfrac{x}{4 \times 10 - 4 \times 14} = \dfrac{y}{14 \times 3 - 10 \times 5} = \dfrac{1}{5\times 4 - 3 \times 4} \\[1em] \Rightarrow \dfrac{x}{40 - 56} = \dfrac{y}{42 - 50} = \dfrac{1}{20 - 12} \\[1em] \Rightarrow \dfrac{x}{-16} = \dfrac{y}{-8} = \dfrac{1}{8} \\[1em] \Rightarrow \dfrac{x}{-16} = \dfrac{1}{8} \text{ and } \dfrac{y}{-8} = \dfrac{1}{8} \\[1em] \Rightarrow x = \dfrac{-16}{8} \text{ and } y = \dfrac{-8}{8} \\[1em] \Rightarrow x = -2 \text{ and } y = -1.$

Hence, x = -2 and y = -1.