$ Đặt$ $ \frac{x -3}{4} = \frac{y +5}{3} = \frac{z -4}{4} = m$
$⇒ x = 4m +3 ; y = 3m -5 ; z = 5m +4$
$Mà$ $2x -3y +4z = 75$
$⇒ 2.(4m +3) -3.(3m -5) +4.(5m +4) = 75$
$⇒ 8m +6 -9m +15 +20m +16 = 75$
$⇒ 19m +37 = 75$
$⇒ 19m = 38$
$⇒ m = 2$
$⇒ x = 4.2 +3 = 11; y = 3.2 -5 = 1; z = 5.2 +4 = 14$
$Vậy$ $x = 11; y = 1; z = 14$