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

3x − 5y = 19, 7x − 3y = 1

Given,

Equations:

⇒ 3x − 5y - 19 = 0

⇒ 7x − 3y - 1 = 0

By cross-multiplication method,

$\Rightarrow \dfrac{x}{(-5) \times (-1) - (-3) \times (-19)} = \dfrac{y}{(-19) \times (7) - (-1) \times (3)} = \dfrac{1}{(3) \times (-3) - (7) \times (-5)} \\[1em] \Rightarrow \dfrac{x}{5 - 57} = \dfrac{y}{-133 + 3} = \dfrac{1}{-9 + 35} \\[1em] \Rightarrow \dfrac{x}{-52} = \dfrac{y}{-130} = \dfrac{1}{26} \\[1em] \Rightarrow \dfrac{x}{-52} = \dfrac{1}{26} \text{ and } \dfrac{y}{-130} = \dfrac{1}{26} \\[1em] \Rightarrow x = \dfrac{-52}{26} \text{ and } y = \dfrac{-130}{26} \\[1em] \Rightarrow x = -2 \text{ and } y = -5.$

Hence, x = -2 and y = -5.