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)

1 answer

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 \((1, 7)\).