Ta có : $42x=60y$
$⇒7x = 10y$
$⇒ \dfrac{x}{10} = \dfrac{y}{7}(1)$
Lại có : $60y = 35z$
$⇒12y = 7z $
$⇒\dfrac{y}{7} = \dfrac{z}{12} (2)$
Từ $(1), (2) ⇒ \dfrac{x}{10} =\dfrac{y}{7}=\dfrac{z}{12} = k$
$⇒x=10k,y=7k,z=12k$
Khi đó : $x+y-z=60$
$⇔10k+7k-12k = 60$
$⇔5k = 60$
$⇔k=12$
$⇒x = 12.10 =120, y = 7.12 = 84, z = 12.12 = 144$
Vậy $(x,y,z) = (120,84,144)$