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

5x − 4y + 2 = 0, 2x + 3y = 13

Given,

Equations :

⇒ 5x − 4y + 2 = 0

⇒ 2x + 3y - 13 = 0

By cross-multiplication method,

$\Rightarrow \dfrac{x}{(-4) \times (-13) - (3) \times (2)} = \dfrac{y}{(2) \times (2) - (-13) \times (5)} = \dfrac{1}{(5) \times (3) - (2) \times (-4)} \\[1em] \Rightarrow \dfrac{x}{(52) - 6} = \dfrac{y}{4 + 65} = \dfrac{1}{15 + 8} \\[1em] \Rightarrow \dfrac{x}{46} = \dfrac{y}{69} = \dfrac{1}{23} \\[1em] \Rightarrow \dfrac{x}{46} = \dfrac{1}{23} \text{ and } \dfrac{y}{69} = \dfrac{1}{23} \\[1em] \Rightarrow x = \dfrac{46}{23} \text{ and } y = \dfrac{69}{23} \\[1em] \Rightarrow x = 2 \text{ and } y = 3.$

Hence, x = 2 and y = 3.