Solve, using cross-multiplication :

3x + 4y = 11

2x + 3y = 8

Given, equations :

⇒ 3x + 4y = 11 and 2x + 3y = 8

⇒ 3x + 4y - 11 = 0 …….(1)

⇒ 2x + 3y - 8 = 0 ……..(2)

By cross-multiplication method :

$\Rightarrow \dfrac{x}{4 \times (-8) - 3 \times (-11)} = \dfrac{y}{(-11) \times 2 - (-8) \times 3} = \dfrac{1}{3 \times 3 - 2 \times 4} \\[1em] \Rightarrow \dfrac{x}{-32 + 33} = \dfrac{y}{-22 + 24} = \dfrac{1}{9 - 8} \\[1em] \Rightarrow \dfrac{x}{1} = \dfrac{y}{2} = \dfrac{1}{1} \\[1em] \Rightarrow x = \dfrac{y}{2} = 1 \\[1em] \Rightarrow x = 1 \text{ and } \dfrac{y}{2} = 1 \\[1em] \Rightarrow x = 1 \text{ and } y = 2.$

Hence, x = 1 and y = 2.