Solve, using cross-multiplication :

8x + 5y = 9

3x + 2y = 4

Given, equations :

⇒ 8x + 5y = 9 and 3x + 2y = 4

⇒ 8x + 5y - 9 = 0 ……….(1)

⇒ 3x + 2y - 4 = 0 ………(2)

By cross-multiplication method we have :

$\Rightarrow \dfrac{x}{5 \times (-4) - 2 \times (-9)} = \dfrac{y}{(-9) \times 3 - (-4) \times 8} = \dfrac{1}{8 \times 2 - 3 \times 5} \\[1em] \Rightarrow \dfrac{x}{-20 + 18} = \dfrac{y}{-27 + 32} = \dfrac{1}{16 - 15} \\[1em] \Rightarrow \dfrac{x}{-2} = \dfrac{y}{5} = \dfrac{1}{1} \\[1em] \Rightarrow \dfrac{x}{-2} = \dfrac{1}{1} \text{ and } \dfrac{y}{5} = \dfrac{1}{1} \\[1em] \Rightarrow x = \dfrac{-2}{1} \text{ and } y = \dfrac{5}{1} \\[1em] \Rightarrow x = -2 \text{ and } y = 5.$

Hence, x = -2 and y = 5.