Alright, let's solve the problem step-by-step.
We are given four pairs of values for \( x \) and \( y \), and we need to determine which pair satisfies the equation \( 2x + 3 = y - 4 \).
The pairs we need to check are:
1. \( x = 3, y = 11 \)
2. \( x = 5, y = 5 \)
3. \( x = 7, y = 9 \)
4. \( x = 9, y = 7 \)
For each pair, we'll substitute the values of \( x \) and \( y \) into the equation and check if both sides are equal.
### Pair 1: \( x = 3, y = 11 \)
Substitute \( x = 3 \) and \( y = 11 \):
[tex]\[ 2(3) + 3 = 11 - 4 \][/tex]
[tex]\[ 6 + 3 = 7 \][/tex]
[tex]\[ 9 = 7 \][/tex]
This pair does not satisfy the equation.
### Pair 2: \( x = 5, y = 5 \)
Substitute \( x = 5 \) and \( y = 5 \):
[tex]\[ 2(5) + 3 = 5 - 4 \][/tex]
[tex]\[ 10 + 3 = 1 \][/tex]
[tex]\[ 13 = 1 \][/tex]
This pair does not satisfy the equation.
### Pair 3: \( x = 7, y = 9 \)
Substitute \( x = 7 \) and \( y = 9 \):
[tex]\[ 2(7) + 3 = 9 - 4 \][/tex]
[tex]\[ 14 + 3 = 5 \][/tex]
[tex]\[ 17 = 5 \][/tex]
This pair does not satisfy the equation.
### Pair 4: \( x = 9, y = 7 \)
Substitute \( x = 9 \) and \( y = 7 \):
[tex]\[ 2(9) + 3 = 7 - 4 \][/tex]
[tex]\[ 18 + 3 = 3 \][/tex]
[tex]\[ 21 = 3 \][/tex]
This pair does not satisfy the equation.
After checking all the pairs, none of them satisfy the equation \( 2x + 3 = y - 4 \).
Therefore, there are no pairs of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] from the given options that justify the claim that the two triangles are congruent.
