Final answer:
None of the given options (a), (b), (c), or (d) represent the equivalent system to the given equations 3x + 3y - 4x + 4y = 0. After simplifying the original equation, we get x - 7y = 0, which does not match any of the answer choices.
Step-by-step explanation:
The student has asked to find the equivalent system of equations for the given system: 3x + 3y - 4x + 4y = 0 and = -8. First, let's simplify the first equation. By combining like terms, we get -x + 7y = 0. If we multiply both sides of this equation by -1, we obtain the equivalent equation: x - 7y = 0. This manipulation does not change the solution set of the equation and is therefore an equivalent transformation. However, each of the given answer options must also be analyzed to see if any represent the same line as the given system.
After reviewing the options given, none of them are equivalent to the system of equations represented by x - 7y = 0. Therefore, none of the answer choices (a), (b), (c), or (d) are equivalent to the given system of equations. A mistake might have been made in the question, or there may be a typo in the provided options.