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

2x + 3y = 17, 3x − 2y = 6

Given,

Equations:

⇒ 2x + 3y - 17 = 0

⇒ 3x - 2y - 6 = 0

By cross-multiplication method,

$\Rightarrow \dfrac{x}{(3) \times (-6) - (-2) \times (-17)} = \dfrac{y}{(-17) \times (3) - (-6) \times (2)} = \dfrac{1}{(2) \times (-2) - (3) \times (3)} \\[1em] \Rightarrow \dfrac{x}{(-18) - 34} = \dfrac{y}{-51 + 12} = \dfrac{1}{-4 - 9} \\[1em] \Rightarrow \dfrac{x}{-52} = \dfrac{y}{-39} = \dfrac{1}{-13} \\[1em] \Rightarrow \dfrac{x}{-52} = \dfrac{1}{-13} \text{ and } \dfrac{y}{-39} = \dfrac{1}{-13} \\[1em] \Rightarrow x = \dfrac{-52}{-13} \text{ and } y = \dfrac{-39}{-13} \\[1em] \Rightarrow x = 4 \text{ and } y = 3.$

Hence, x = 4 and y = 3.