Solve the following pair of linear equations by the elimination method and the substitution method :

3x - 5y - 4 = 0 and 9x = 2y + 7

Given,

⇒ 3x - 5y - 4 = 0

⇒ 3x - 5y = 4 ……….(1)

⇒ 9x = 2y + 7

⇒ 9x - 2y = 7 ……….(2)

Multiplying equation (1) by 3, we get :

9x - 15y = 12 ……….(3)

Subtracting equation (3) from (2), we get :

⇒ 9x - 2y - (9x - 15y) = 7 - 12

⇒ 9x - 9x - 2y + 15y = -5

⇒ 13y = -5

⇒ y = $-\dfrac{5}{13}$.

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

$\Rightarrow 3x - 5 \times -\dfrac{5}{13} = 4 \\[1em] \Rightarrow 3x + \dfrac{25}{13} = 4 \\[1em] \Rightarrow 3x = 4 - \dfrac{25}{13} \\[1em] \Rightarrow 3x = \dfrac{52 - 25}{13} \\[1em] \Rightarrow 3x = \dfrac{27}{13} \\[1em] \Rightarrow x = \dfrac{27}{3 \times 13} \\[1em] \Rightarrow x = \dfrac{9}{13}.$

Hence, x = $\dfrac{9}{13}\text{ and y} = -\dfrac{5}{13}$.