On comparing the ratios find out whether the following pair of linear equations are consistent, or inconsistent. (4/3) x + 2y = 8 ; 2x + 3y = 12

Given, Equations : 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 a 1 x + b 1 y + c 1 = 0 and a 2 x + b 2 y + c 2 = 0 respectively, we get : a 1 = 4, b 1 = 6, c 1 = -24, a 2 = 2, b 2 = 3 and c 2 = -12. Since, . Hence, the set of linear equations are consistent.