Find the ordered triple (x,y,z) that satisfies the following system: x−2y=0y−2z=0x+z=5.
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
