Solve, using cross-multiplication :

x - y + 2 = 0

7x + 9y = 130

Given, equations :

⇒ x - y + 2 = 0 and 7x + 9y = 130

⇒ x - y + 2 = 0 ……..(1)

⇒ 7x + 9y - 130 = 0 ……..(2)

By cross-multiplication method :

$\Rightarrow \dfrac{x}{(-1) \times (-130) - 9 \times 2} = \dfrac{y}{2 \times 7 - 1 \times (-130)} = \dfrac{1}{1 \times 9 - 7 \times (-1)} \\[1em] \Rightarrow \dfrac{x}{130 - 18} = \dfrac{y}{14 + 130} = \dfrac{1}{9 + 7} \\[1em] \Rightarrow \dfrac{x}{112} = \dfrac{y}{144} = \dfrac{1}{16} \\[1em] \Rightarrow \dfrac{x}{112} = \dfrac{1}{16} \text{ and } \dfrac{y}{144} = \dfrac{1}{16} \\[1em] \Rightarrow x = \dfrac{112}{16} \text{ and } y = \dfrac{144}{16} \\[1em] \Rightarrow x = 7 \text{ and } y = 9.$

Hence, x = 7 and y = 9.