Solve the following pairs of linear (simultaneously) equations using method of elimination by substitution:

6x = 7y + 7
7y - x = 8

Given,

Equations : 6x = 7y + 7 and 7y - x = 8

⇒ 7y - x = 8

⇒ x = 7y - 8 ………(1)

Substituting value of x from equation (1) in 6x = 7y + 7, we get :

⇒ 6(7y - 8) = 7y + 7

⇒ 42y - 48 = 7y + 7

⇒ 42y - 7y = 7 + 48

⇒ 35y = 55

⇒ y = $\dfrac{55}{35} = \dfrac{11}{7}$.

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

$\Rightarrow x = 7 \times \dfrac{11}{7} - 8 \\[1em] \Rightarrow x = 11 - 8 = 3.$

Hence, x = 3 and y = $\dfrac{11}{7}$.