The solution to the given system of equations is \(\mathrm{(x, y)}\). What is the value of x? y = 4...

1. TRANSLATE the problem information

• Given system:
  • \(\mathrm{y = 4}\)
  • \(\mathrm{x = y + 6}\)
• What we need: The value of x

2. INFER the solution strategy

• Since the first equation directly gives us \(\mathrm{y = 4}\), we can substitute this value into the second equation
• This will give us x in terms of known values

3. SIMPLIFY by substitution

• Take the second equation: \(\mathrm{x = y + 6}\)
• Substitute \(\mathrm{y = 4}\): \(\mathrm{x = 4 + 6}\)
• Calculate: \(\mathrm{x = 10}\)

Answer: A. 10

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misread what the problem is asking for and provide the value of y instead of x.

Since \(\mathrm{y = 4}\) is clearly stated in the first equation, students might think this is the answer without carefully reading that the problem asks for x. This may lead them to select Choice C (4).

Second Most Common Error:

Inadequate SIMPLIFY execution: Students make basic arithmetic errors when performing the substitution.

For example, they might incorrectly calculate \(\mathrm{4 + 6}\) or confuse the operation, leading to answers like 2 (\(\mathrm{4 - 6 + 4}\)) or 6. This confusion about the arithmetic may lead them to select Choice B (6) or Choice D (2).

The Bottom Line:

This problem tests whether students can carefully follow instructions about which variable to solve for and execute a simple substitution correctly. The system itself is straightforward, but attention to detail is crucial.