Solve the following simultaneous equations:

7x - 2y = 20, 11x + 15y + 23 = 0

Given,

Equations : 7x - 2y = 20, 11x + 15y + 23 = 0

⇒ 7x - 2y = 20

⇒ 7x = 20 + 2y

⇒ x = $\dfrac{20 + 2y}{7}$     ….(1)

Substituting value of x from equation (1) in 11x + 15y + 23 = 0, we get :

$\Rightarrow 11\Big(\dfrac{20 + 2y}{7}\Big) + 15y + 23 = 0 \\[1em] \Rightarrow \Big(\dfrac{220 + 22y}{7}\Big) + 15y + 23 = 0 \\[1em] \Rightarrow \Big(\dfrac{220 + 22y + 105y + 161}{7}\Big) = 0 \\[1em] \Rightarrow 381 + 127y = 0 \\[1em] \Rightarrow 127y = - 381 \\[1em] \Rightarrow y = \dfrac{-381}{127}\\[1em] \Rightarrow y = -3.$

Substituting value of y in equation (1), we get :

$\Rightarrow x = \dfrac{20 + 2y}{7} \\[1em] \Rightarrow x = \dfrac{20 + 2(-3)}{7} \\[1em] \Rightarrow x = \dfrac{20 - 6}{7} \\[1em] \Rightarrow x = \dfrac{14}{7} \\[1em] \Rightarrow x = 2.$

Hence, x = 2, y = -3.