What is the solution (r, s) to the given system of equations?s + 7r = 27r = 3

1. TRANSLATE the problem information

• Given system:
  • \(\mathrm{s + 7r = 27}\)
  • \(\mathrm{r = 3}\)
• Find: solution \(\mathrm{(r, s)}\) as an ordered pair

2. INFER the most efficient approach

• Since the second equation directly tells us \(\mathrm{r = 3}\), we don't need elimination or complex manipulation
• Strategy: Substitute \(\mathrm{r = 3}\) into the first equation to find s

3. SIMPLIFY through substitution

• Substitute \(\mathrm{r = 3}\) into \(\mathrm{s + 7r = 27}\):

\(\mathrm{s + 7(3) = 27}\)

• Multiply:

\(\mathrm{s + 21 = 27}\)

• Subtract 21 from both sides:

\(\mathrm{s = 6}\)

4. TRANSLATE the final answer format

• We found \(\mathrm{r = 3}\) and \(\mathrm{s = 6}\)
• The problem asks for solution \(\mathrm{(r, s)}\), so: \(\mathrm{(3, 6)}\)

Answer: B. \(\mathrm{(3, 6)}\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Confusing the order of coordinates in the solution format

Students correctly find \(\mathrm{r = 3}\) and \(\mathrm{s = 6}\), but then write the answer as \(\mathrm{(6, 3)}\) instead of \(\mathrm{(3, 6)}\). They forget that \(\mathrm{(r, s)}\) means r comes first, s comes second in the ordered pair.

This leads them to select Choice A. \(\mathrm{(6, 3)}\)

Second Most Common Error:

Poor SIMPLIFY execution: Making arithmetic errors during substitution

Students substitute correctly but make calculation mistakes: \(\mathrm{s + 7(3) = 27}\) might become \(\mathrm{s + 21 = 24}\) (wrong), leading to \(\mathrm{s = 3}\). Or they might forget to distribute the 7, calculating \(\mathrm{s + 3 = 27}\) instead.

This causes confusion and may lead to guessing among the remaining choices.

The Bottom Line:

This problem tests whether students can carefully track variable order in solutions and execute basic substitution without computational errors. The conceptual demand is low, but precision in both calculation and notation is crucial.