To determine which equations correctly model the total yards of fabric Sophie will buy, let's consider each possible equation given some values from the table.
First, note the pairs of values for \(x\) and \(y\):
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Red fabric } (x \, \text{yards}) & \text{Blue fabric } (y \, \text{yards}) \\
\hline
1 & 27 \\
2 & 26 \\
3 & 25 \\
4 & 24 \\
\hline
\end{array}
\][/tex]
We'll use the pairs (1, 27) and check the validity of each equation step-by-step.
1. Equation: \(x + y = 28\)
- \(x = 1\)
- \(y = 27\)
Check: \(1 + 27 = 28\)
- Result: True
2. Equation: \(28 + x = y\)
- \(x = 1\)
- \(y = 27\)
Check: \(28 + 1 = 27\)
- Result: False
3. Equation: \(x - y = 2\)
- \(x = 1\)
- \(y = 27\)
Check: \(1 - 27 = 2\)
- Result: False
4. Equation: \(28 - x = y\)
- \(x = 1\)
- \(y = 27\)
Check: \(28 - 1 = 27\)
- Result: True
5. Equation: \(28 - y = x\)
- \(x = 1\)
- \(y = 27\)
Check: \(28 - 27 = 1\)
- Result: True
Based on the evaluations, the equations that correctly model the total yards of fabric Sophie will buy are:
1. \(x + y = 28\)
4. \(28 - x = y\)
5. \(28 - y = x\)
So the valid equations from the given list are:
- \(x + y = 28\)
- \(28 - x = y\)
- [tex]\(28 - y = x\)[/tex]
