Question

What is the value of \( X \)?
I. \( X + 3Y = 9 \)
II. \( 3X + 9Y = 27 \)

• A. If the statement I alone is sufficient to answer the question.
• B. If the statement II alone is sufficient to answer the question.
• C. If the statements I and II together are sufficient to answer the question but neither statement alone is sufficient.
• D. If the statements I and II together are not sufficient to answer the question and additional data is required.

Hint:

When solving systems of linear equations, ensure the equations are consistent and check if one is a multiple of the other to avoid redundant equations.

Answer 1

The Correct Option is D

From the first equation: \[ X + 3Y = 9 \] From the second equation: \[ 3X + 9Y = 27 \] Notice that the second equation is simply three times the first equation: \[ 3(X + 3Y) = 27 \] \[ 3 \times 9 = 27 \] This is true, so the two equations are consistent and provide the same information. Therefore, we can solve for \( X \) using the first equation: \[ X + 3Y = 9 \] Solving for \( X \) in terms of \( Y \): \[ X = 9 - 3Y \] Thus, the value of \( X \) depends on \( Y \), and there is no unique solution for \( X \) without knowing the value of \( Y \). Since this doesn't provide enough information to determine a specific numerical value for \( X \), the correct answer is \( \boxed{4} \).