Determine the Value of x in a System of Equations

Very Hard Problem Solving Algebra

Consider the following system of equations:

$$ 2x + 3y = 12 $$

$$ 4x - y = 6 $$

What is the value of $x$?

Statement (1): $y = 2$.

Statement (2): The product of $x$ and $y$ is equal to 6.

Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

Both statements (1) and (2) together are sufficient, but neither statement alone is sufficient.

Each statement alone is sufficient.

Statements (1) and (2) together are not sufficient.

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