Find the ordered triple $(x,y,z)$ that satisfies the following system: \begin{align*} x-2y&=0\\ y-2z&=0\\ x+z&=5. \end{align*}
x - 2y = 0 ⇒ x = 2y (1)
y - 2z = 0 ⇒ y = 2z ⇒ y/2 = z (2)
x + z = 5 (3)
Put (1) and (2) into (3)
2y + y/2 = 5 multiply through by 2
4y + y = 10
5y = 10 ⇒ y = 2
So x = 2y = 4 and z = y/2 = 1
