The solution to the given system of equations is \(\mathrm{(x, y)}\). What is the value of y?x = 10y =...

1. TRANSLATE the problem information

• Given system of equations:
  • \(\mathrm{x = 10}\)
  • \(\mathrm{y = x + 21}\)
• The question asks: What is the value of y?

2. INFER the solution approach

• Since the first equation directly gives us \(\mathrm{x = 10}\), we can substitute this value into the second equation to find y
• This is a perfect setup for the substitution method

3. SIMPLIFY by substituting and calculating

• Substitute \(\mathrm{x = 10}\) into the second equation:
  \(\mathrm{y = x + 21}\)
  \(\mathrm{y = 10 + 21}\)
  \(\mathrm{y = 31}\)

Answer: D. 31

Why Students Usually Falter on This Problem

Most Common Error Path:

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

Since \(\mathrm{x = 10}\) is clearly given in the first equation, they might think this is the answer the question wants. They see "\(\mathrm{x = 10}\)" and select this value without carefully reading that the question asks for y.

This leads them to select Choice B (10).

Second Most Common Error:

Poor SIMPLIFY execution: Students correctly identify that they need to substitute and find y, but make an arithmetic error.

They might miscalculate 10 + 21, or misread the equation as \(\mathrm{y = 21}\) (ignoring the x term entirely), leading to incorrect values.

This may lead them to select Choice C (21) or causes calculation confusion leading to guessing.

The Bottom Line:

This problem tests careful reading and basic substitution skills. The mathematics is straightforward, but students must pay attention to what variable the question is asking for and execute the substitution correctly.