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

2x + 5y = 1, 2x + 3y = 3

Given,

Equations:

⇒ 2x + 5y - 1 = 0

⇒ 2x + 3y - 3 = 0

By cross-multiplication method,

$\Rightarrow \dfrac{x}{(5) \times (-3) - (3) \times (-1)} = \dfrac{y}{(-1) \times (2) - (-3) \times (2)} = \dfrac{1}{(2) \times (3) - (2) \times (5)} \\[1em] \Rightarrow \dfrac{x}{(-15) + 3} = \dfrac{y}{-2 + 6} = \dfrac{1}{6 - 10} \\[1em] \Rightarrow \dfrac{x}{-12} = \dfrac{y}{4} = \dfrac{1}{-4} \\[1em] \Rightarrow \dfrac{x}{-12} = \dfrac{1}{-4} \text{ and } \dfrac{y}{4} = \dfrac{1}{-4} \\[1em] \Rightarrow x = \dfrac{-12}{-4} \text{ and } y = \dfrac{4}{-4} \\[1em] \Rightarrow x = 3 \text{ and } y = -1.$

Hence, x = 3 and y = -1.