Solve, using cross-multiplication :

4x - 3y - 11 = 0

6x + 7y - 5 = 0

Given, equations :

⇒ 4x - 3y - 11 = 0 …………(1)

⇒ 6x + 7y - 5 = 0 …………(2)

By cross-multiplication method :

$\Rightarrow \dfrac{x}{(-3) \times (-5) - 7 \times (-11)} = \dfrac{y}{(-11) \times 6 - (-5) \times 4} = \dfrac{1}{4 \times 7 - 6 \times (-3)} \\[1em] \Rightarrow \dfrac{x}{15 + 77} = \dfrac{y}{-66 + 20} = \dfrac{1}{28+ 18} \\[1em] \Rightarrow \dfrac{x}{92} = \dfrac{y}{-46} = \dfrac{1}{46} \\[1em] \Rightarrow \dfrac{x}{92} = \dfrac{1}{46} \text{ and } \dfrac{y}{-46} = \dfrac{1}{46} \\[1em] \Rightarrow x = \dfrac{92}{46} \text{ and } y = \dfrac{-46}{46} \\[1em] \Rightarrow x = 2 \text{ and } y = -1.$

Hence, x = 2 and y = -1.