On comparing the ratios $\dfrac{a$1}{a2}, \dfrac{b1}{b2}, \dfrac{c1}{c2} find out whether the following pair of linear equations are consistent, or inconsistent.

$\dfrac{4}{3}x + 2y = 8; 2x + 3y = 12$

Given,

Equations : $\dfrac{4}{3}x + 2y = 8; 2x + 3y = 12$ or,

⇒ 4x + 6y = 24; 2x + 3y = 12

⇒ 4x + 6y - 24 = 0 ; 2x + 3y - 12 = 0.

Comparing equations 4x + 6y - 24 = 0 and 2x + 3y - 12 = 0 with a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 respectively, we get :

a₁ = 4, b₁ = 6, c₁ = -24, a₂ = 2, b₂ = 3 and c₂ = -12.

$\dfrac{a$1}{a2} = \dfrac{4}{2} = 2

$\dfrac{b$1}{b2} = \dfrac{6}{3} = 2

$\dfrac{c$1}{c2} = \dfrac{-24}{-12} = 2

Since, $\dfrac{a$1}{a2} = \dfrac{b1}{b2} = \dfrac{c1}{c2}.

Hence, the set of linear equations are consistent.