Question

Which of the following ordered pairs is part of the solution set for the equation y = 2x + 5'
(1, 2)
(7, 1)
(3, - 1)
(1, 7)

Answer 1

To determine which ordered pairs are 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 check if the resulting \( y \) value matches the given \( y \) in the pair.

1. For the pair \( (1, 2) \):
\[
y = 2(1) + 5 = 2 + 5 = 7
\]
The pair \( (1, 2) \) does not satisfy the equation (7 ≠ 2).

2. For the pair \( (7, 1) \):
\[
y = 2(7) + 5 = 14 + 5 = 19
\]
The pair \( (7, 1) \) does not satisfy the equation (19 ≠ 1).

3. For the pair \( (3, -1) \):
\[
y = 2(3) + 5 = 6 + 5 = 11
\]
The pair \( (3, -1) \) does not satisfy the equation (11 ≠ -1).

4. For the pair \( (1, 7) \):
\[
y = 2(1) + 5 = 2 + 5 = 7
\]
The pair \( (1, 7) \) satisfies the equation (7 = 7).

Therefore, the ordered pair that is part of the solution set for the equation \( y = 2x + 5 \) is \( \boxed{(1, 7)} \).