$\dfrac{z - 5}{6} = \dfrac{x - 1}{2} = \dfrac{y + 3}{4}$
⇔$\dfrac{5(z-5)}{30} = \dfrac{3(x -1)}{6} = \dfrac{4(y + 3)}{16}$
⇔ $\dfrac{5z - 25}{30} = \dfrac{3x - 3}{6} = \dfrac{4y + 12}{16}$
Áp dụng t/c dãy TSBN ta có:
$\dfrac{5z - 25}{30} = \dfrac{3x - 3}{6} = \dfrac{4y + 12}{16}$
$= \dfrac{(5z - 25) - (3x - 3) - (4y + 12)}{30 - 6 - 16}$
$=\dfrac{(5z - 3x - 4y) + (3 - 25 - 12)}{8}$
$=\dfrac{50 - 34}{8}$
$= 2$
Do đó: $5z - 25 = 2 . 30 = 60 ⇔ 5z = 85 ⇔ z = 17$
$3x - 3 = 2. 6 = 12 ⇔ 3x = 15 ⇔ x = 5$
$4y + 12 = 2. 16 = 32 ⇔ 4y = 20 ⇔ y = 5$
Vậy x = 5; y = 5; z = 17
