7x - 4y = -84 For the given equation, which table gives three values of x and their corresponding values...

1. TRANSLATE the problem information

• Given: Linear equation \(7x - 4y = -84\)
• Need: Which table contains \((x,y)\) pairs that satisfy this equation
• Four tables with different coordinate pairs to test

2. INFER the solution strategy

• To verify a table is correct, ALL coordinate pairs must satisfy the equation
• Test each table by substituting x and y values into \(7x - 4y = -84\)
• Stop testing a table once you find a pair that doesn't work

3. SIMPLIFY by testing Table A systematically

• Test \((0, 21)\): \(7(0) - 4(21) = 0 - 84 = -84\) ✓
• Test \((4, 28)\): \(7(4) - 4(28) = 28 - 112 = -84\) ✓
• Test \((8, 35)\): \(7(8) - 4(35) = 56 - 140 = -84\) ✓
• All three pairs work!

4. SIMPLIFY by testing Table B to confirm

• Test \((0, 35)\): \(7(0) - 4(35) = 0 - 140 = -140 eq -84\) ✗
• This table fails immediately

Answer: A

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Students make arithmetic errors, especially when working with negative numbers and subtraction.

For example, they might calculate \(7(8) - 4(35)\) as \(56 - 140 = 84\) instead of \(-84\), missing the negative sign. Or they might make errors in multiplication like \(4(28) = 102\) instead of \(112\). These calculation mistakes lead them to incorrectly reject the right table or accept a wrong one.

This leads to confusion and guessing among the answer choices.

The Bottom Line:

Success requires careful, systematic arithmetic with negative numbers. Students who rush through calculations or aren't careful with signs will struggle to identify the correct table reliably.