Find the ordered triple (x,y,z) that satisfies the following system: x-2y=0, y-2z=0, x+z=5.
+23246 x - 2y = 0 ---> x = 2y
Substituting: since x + z = 5 and x = 2y ---> 2y + z = 5
Combining 2y + z = 5 and y - 2z = 0
2y + z = 5 ---> x 2 ---> 4y + 2z = 10
y - 2z = 0 ---> y - 2z = 0
Adding down: 5y = 10 ---> y = 2
Since y = 2 ---> x = 2y ---> x = 2(2) ---> x = 4
Since x = 4 ---> x + z = 5 ---> 4 + z = 5 ---> z = 1
+23246 x - 2y = 0 ---> x = 2y
Substituting: since x + z = 5 and x = 2y ---> 2y + z = 5
Combining 2y + z = 5 and y - 2z = 0
2y + z = 5 ---> x 2 ---> 4y + 2z = 10
y - 2z = 0 ---> y - 2z = 0
Adding down: 5y = 10 ---> y = 2
Since y = 2 ---> x = 2y ---> x = 2(2) ---> x = 4
Since x = 4 ---> x + z = 5 ---> 4 + z = 5 ---> z = 1
