To determine which pair of values for \( x \) and \( y \) makes the expression \( 2x + 3 \) equal to \( y - 4 \), we will evaluate each given pair step by step.
Let's introduce the number pairs one by one and check if the expressions match:
1. Pair 1: \( x = 3 \), \( y = 11 \):
- Calculate \( 2x + 3 \):
\( 2(3) + 3 = 6 + 3 = 9 \)
- Calculate \( y - 4 \):
\( 11 - 4 = 7 \)
The results are:
[tex]\[
2x + 3 = 9 \quad \text{and} \quad y - 4 = 7
\][/tex]
Since \( 9 \neq 7 \), our condition is not met with this pair.
2. Pair 2: \( x = 5 \), \( y = 5 \):
- Calculate \( 2x + 3 \):
\( 2(5) + 3 = 10 + 3 = 13 \)
- Calculate \( y - 4 \):
\( 5 - 4 = 1 \)
The results are:
[tex]\[
2x + 3 = 13 \quad \text{and} \quad y - 4 = 1
\][/tex]
Since \( 13 \neq 1 \), our condition is not met with this pair.
3. Pair 3: \( x = 7 \), \( y = 9 \):
- Calculate \( 2x + 3 \):
\( 2(7) + 3 = 14 + 3 = 17 \)
- Calculate \( y - 4 \):
\( 9 - 4 = 5 \)
The results are:
[tex]\[
2x + 3 = 17 \quad \text{and} \quad y - 4 = 5
\][/tex]
Since \( 17 \neq 5 \), our condition is not met with this pair.
4. Pair 4: \( x = 9 \), \( y = 7 \):
- Calculate \( 2x + 3 \):
\( 2(9) + 3 = 18 + 3 = 21 \)
- Calculate \( y - 4 \):
\( 7 - 4 = 3 \)
The results are:
[tex]\[
2x + 3 = 21 \quad \text{and} \quad y - 4 = 3
\][/tex]
Since \( 21 \neq 3 \), our condition is not met with this pair.
Since none of the given pairs satisfies the condition [tex]\( 2x + 3 = y - 4 \)[/tex], there is no pair that justifies the claim that the two triangles are congruent based on the provided pairs.
