Question

Which of the following ordered pairs is part of the solution set for the equation y=2x+5 ?

(1 point)
Responses

(7,1)
left parenthesis 7 comma 1 right parenthesis

(1,7)
left parenthesis 1 comma 7 right parenthesis

(1,2)
left parenthesis 1 comma 2 right parenthesis

(3,−1)

Answer 1

To determine which ordered pair is part of the solution set for the equation \( y = 2x + 5 \), we need to substitute the \( x \)-value from each pair into the equation and see if it produces the corresponding \( y \)-value.

1. **For (7, 1)**:
- Substitute \( x = 7 \):
\[
y = 2(7) + 5 = 14 + 5 = 19
\]
- This gives \( y = 19 \neq 1\).

2. **For (1, 7)**:
- Substitute \( x = 1 \):
\[
y = 2(1) + 5 = 2 + 5 = 7
\]
- This gives \( y = 7\), which matches the pair.

3. **For (1, 2)**:
- Substitute \( x = 1 \):
\[
y = 2(1) + 5 = 2 + 5 = 7
\]
- This gives \( y = 7 \neq 2\).

4. **For (3, -1)**:
- Substitute \( x = 3 \):
\[
y = 2(3) + 5 = 6 + 5 = 11
\]
- This gives \( y = 11 \neq -1\).

The only pair that satisfies the equation \( y = 2x + 5 \) is \((1, 7)\).

Thus, the answer is \((1, 7)\).