Final answer:
The ordered pair (4, -2) is a solution of the given system of equations.
Step-by-step explanation:
To determine whether the given ordered pair is a solution of the system, we substitute the values of x and y in both equations and check if the equations are satisfied.
For the first equation, x - y = 6, when we substitute x = 4 and y = -2, we get 4 - (-2) = 6 which is true. So, the ordered pair satisfies the first equation.
Similarly, for the second equation, 6x - 3y = 30, when we substitute x = 4 and y = -2, we get 6(4) - 3(-2) = 30 which is also true. So, the ordered pair satisfies the second equation as well.
Since the ordered pair satisfies both equations in the system, we can conclude that (4, -2) is indeed a solution of the system.