The correct answer is:

D. Substitution; Equation II can be solved for x in one step by subtracting 3y from both sides.

Explanation:

To decide the appropriate method, let’s review each option in light of the system of equations:

1. Option A: "Elimination; a coefficient in Equation I is an integer multiple of a coefficient in Equation II."

   • This is incorrect because none of the coefficients in Equation I are multiples of the corresponding coefficients in Equation II (for example, 4 is not a multiple of 2, and -5 is not a multiple of 3).

2. Option B: "Elimination; a coefficient in Equation II is an integer multiple of a coefficient in Equation I."

   • This is also incorrect for the same reason as above. None of the coefficients in Equation II are integer multiples of those in Equation I.

3. Option C: "Substitution; Equation I can be solved for x in one step by dividing both sides by 4."

   • This is incorrect because solving for $x$ in Equation I would require additional steps beyond dividing by 4. We would first need to isolate $x$ by adding or subtracting terms.

4. Option D: "Substitution; Equation II can be solved for x in one step by subtracting 3y from both sides."

   • This is correct. In Equation II, we can isolate $x$ by subtracting $3y$ from both sides to get: $2x = 2 - 3y$
   • This allows for substitution directly by isolating $x$ after an additional division by 2.

Final Answer: D

Would you like a breakdown of solving this system or further clarification?

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Related Questions:

1. How does the elimination method work for systems of equations?
2. What are common indicators that substitution is the best method for solving a system?
3. What steps would be involved if we chose the elimination method for this system?
4. Can we solve this system using matrix methods?
5. How does graphing the equations provide a solution to this system?

Tip: When deciding between elimination and substitution, look at the complexity of isolating one variable—if one equation can isolate a variable easily, substitution is often advantageous.