Solve, using cross-multiplication :

4x - y = 5

5y - 4x = 7

Given, equations :

⇒ 4x - y = 5 and 5y - 4x = 7

⇒ 4x - y - 5 = 0 ……….(1)

⇒ -4x + 5y - 7 = 0 ………(2)

By cross-multiplication method :

$\Rightarrow \dfrac{x}{(-1) \times (-7) - 5 \times (-5)} = \dfrac{y}{(-5) \times (-4) - (-7) \times 4} = \dfrac{1}{4 \times 5 - (-4) \times (-1)} \\[1em] \Rightarrow \dfrac{x}{7 + 25} = \dfrac{y}{20 + 28} = \dfrac{1}{20 - 4} \\[1em] \Rightarrow \dfrac{x}{32} = \dfrac{y}{48} = \dfrac{1}{16} \\[1em] \Rightarrow \dfrac{x}{32} = \dfrac{1}{16} \text{ and } \dfrac{y}{48} = \dfrac{1}{16} \\[1em] \Rightarrow x = \dfrac{32}{16} \text{ and } y = \dfrac{48}{16} \\[1em] \Rightarrow x = 2 \text{ and } y = 3.$

Hence, x = 2 and y = 3.