To determine which of the ordered pairs is part of the solution set for the equation \( Y = 2x + 5 \), we can substitute the \( x \)-value from each ordered pair into the equation and see if it gives the corresponding \( y \)-value.
Let's check each option:
A. \( (1, 7) \)
- Substitute \( x = 1 \): \[ Y = 2(1) + 5 = 2 + 5 = 7 \]
- The pair is \( (1, 7) \), which matches. So this pair is a solution.
B. \( (7, 1) \)
- Substitute \( x = 7 \): \[ Y = 2(7) + 5 = 14 + 5 = 19 \]
- The pair is \( (7, 1) \), which does not match. So this pair is not a solution.
C. \( (3, -1) \)
- Substitute \( x = 3 \): \[ Y = 2(3) + 5 = 6 + 5 = 11 \]
- The pair is \( (3, -1) \), which does not match. So this pair is not a solution.
D. \( (1, 2) \)
- Substitute \( x = 1 \): \[ Y = 2(1) + 5 = 2 + 5 = 7 \]
- The pair is \( (1, 2) \), which does not match. So this pair is not a solution.
From the checks, the only ordered pair that is part of the solution set for the equation \( Y = 2x + 5 \) is:
A. \( (1, 7) \).