Solve, using cross-multiplication :

6x + 7y - 11 = 0

5x + 2y = 13

Given, equations :

⇒ 6x + 7y - 11 = 0 and 5x + 2y = 13

⇒ 6x + 7y - 11 = 0 ……..(1)

⇒ 5x + 2y - 13 = 0 ……..(2)

By cross-multiplication method :

$\Rightarrow \dfrac{x}{7 \times (-13) - 2 \times (-11)} = \dfrac{y}{(-11) \times 5 - (-13) \times 6} = \dfrac{1}{6 \times 2 - 5 \times 7} \\[1em] \Rightarrow \dfrac{x}{-91 + 22} = \dfrac{y}{-55 + 78} = \dfrac{1}{12 - 35} \\[1em] \Rightarrow \dfrac{x}{-69} = \dfrac{y}{23} = \dfrac{1}{-23} \\[1em] \Rightarrow \dfrac{x}{-69} = \dfrac{1}{-23} \text{ and } \dfrac{y}{23} = \dfrac{1}{-23} \\[1em] \Rightarrow x = \dfrac{-69}{-23} \text{ and } y = \dfrac{23}{-23}\\[1em] \Rightarrow x = 3 \text{ and } y = -1.$

Hence, x = 3 and y = -1.