Step 1 :Define the ordered pair (2,6) as (x,y).
Step 2 :Substitute (x,y) into the first equation -3x + y = 0, we get -3*2 + 6 = 0, which is true.
Step 3 :Substitute (x,y) into the second equation 2x + y = -2, we get 2*2 + 6 = -2, which is false.
Step 4 :Since the ordered pair (2,6) satisfies the first equation but does not satisfy the second equation, it is not a solution to the system of equations.
Step 5 :Final Answer: The ordered pair (2,6) is \(\boxed{not}\) a solution to the system of equations.