Step 1: Extract the given ordered pair and the equations from the statement. The ordered pair is (6, -4) and the equations are -x - 2y = 2 and x + 3y = 0.
Step 2: For the first equation, substitute x = 6 and y = -4. This gives us -6 - 2*(-4) which results in -6 + 8 = 2. This matches with the constant right side of the equation, i.e., 2.
So, yes, the ordered pair (6, -4) is a solution to the first equation.
Step 3: For the second equation, again substitute x = 6 and y = -4. We get 6 + 3*(-4) is equal to -6 which doesn't match with the constant right side of the equation, i.e., 0.
This implies that the ordered pair (6, -4) is not a solution to the second equation.
Conclusion: Although the ordered pair (6, -4) is a solution to the first equation, it is not a solution to the second equation. Therefore, the ordered pair (6, -4) is not a solution for the given system of equations.