Solve the following system of equations by using the method of cross multiplication:

2x − 5y + 8 = 0, x − 4y + 7 = 0

Given,

Equations:

⇒ 2x − 5y + 8 = 0

⇒ x − 4y + 7 = 0

By cross-multiplication method,

$\Rightarrow \dfrac{x}{(-5) \times (7) - (-4) \times (8)} = \dfrac{y}{(8) \times (1) - (7) \times (2)} = \dfrac{1}{(2) \times (-4) - (1) \times (-5)} \\[1em] \Rightarrow \dfrac{x}{(-35) + 32} = \dfrac{y}{8 - 14} = \dfrac{1}{-8 + 5} \\[1em] \Rightarrow \dfrac{x}{-3} = \dfrac{y}{-6} = \dfrac{1}{-3} \\[1em] \Rightarrow \dfrac{x}{-3} = \dfrac{1}{-3} \text{ and } \dfrac{y}{-6} = \dfrac{1}{-3} \\[1em] \Rightarrow x = \dfrac{-3}{-3} \text{ and } y = \dfrac{-6}{-3} \\[1em] \Rightarrow x = 1 \text{ and } y = 2.$

Hence, x = 1 and y = 2.