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

7x − 2y = 20, 11x + 15y + 23 = 0

Given,

Equations:

⇒ 7x − 2y - 20 = 0

⇒ 11x + 15y + 23 = 0

By cross-multiplication method,

$\Rightarrow \dfrac{x}{(-2) \times (23) - (15) \times (-20)} = \dfrac{y}{(-20) \times (11) - (23) \times (7)} = \dfrac{1}{(7) \times (15) - (11) \times (-2)} \\[1em] \Rightarrow \dfrac{x}{(-46) + 300} = \dfrac{y}{-220 - 161} = \dfrac{1}{105 + 22} \\[1em] \Rightarrow \dfrac{x}{254} = \dfrac{y}{-381} = \dfrac{1}{127} \\[1em] \Rightarrow \dfrac{x}{254} = \dfrac{1}{127} \text{ and } \dfrac{y}{-381} = \dfrac{1}{127} \\[1em] \Rightarrow x = \dfrac{254}{127} \text{ and } y = \dfrac{-381}{127} \\[1em] \Rightarrow x = 2 \text{ and } y = -3.$

Hence, x = 2 and y = -3.