Solve, using cross-multiplication :

4x - 3y = 0

2x + 3y = 18

Given, equations :

⇒ 4x - 3y = 0 and 2x + 3y = 18

⇒ 4x - 3y = 0 ………(1)

⇒ 2x + 3y - 18 = 0 …..(2)

By cross-multiplication method :

$\Rightarrow \dfrac{x}{(-3) \times (-18) - 3 \times 0} = \dfrac{y}{0 \times 2 - (-18) \times 4} = \dfrac{1}{4 \times 3 - 2 \times (-3)} \\[1em] \Rightarrow \dfrac{x}{54 - 0} = \dfrac{y}{0 + 72} = \dfrac{1}{12 + 6} \\[1em] \Rightarrow \dfrac{x}{54} = \dfrac{y}{72} = \dfrac{1}{18} \\[1em] \Rightarrow \dfrac{x}{54} = \dfrac{1}{18} \text{ and } \dfrac{y}{72} = \dfrac{1}{18} \\[1em] \Rightarrow x = \dfrac{54}{18} \text{ and } y = \dfrac{72}{18}\\[1em] \Rightarrow x = 3 \text{ and } y = 4.$

Hence, x = 3 and y = 4.