Question

Which statement about the ordered pairs (−9, 3) and (2, −4) is true for the equation 6x−y2=14?

Responses

(2, −4) is a solution to the equation.
Begin ordered pair 2 comma negative 4 end orderd pair is a solution to the equation.

Neither ordered pair is a solution.
Neither ordered pair is a solution.

(−9, 3) is a solution to the equation.
Begin ordered pair negative 9 comma 3 end orderd pair is a solution to the equation.

Both ordered pairs are solutions.
Both ordered pairs are solutions.

Answer 1

To determine which statement is true regarding the ordered pairs (−9, 3) and (2, −4) for the equation \(6x - y^2 = 14\), we need to substitute each pair into the equation.

1. **For the ordered pair \((-9, 3)\):**

Substitute \(x = -9\) and \(y = 3\) into the equation:
\[
6(-9) - (3)^2 = 14
\]
\[
-54 - 9 = 14
\]
\[
-63 \neq 14
\]
Therefore, \((-9, 3)\) is **not** a solution.

2. **For the ordered pair \((2, -4)\):**

Substitute \(x = 2\) and \(y = -4\) into the equation:
\[
6(2) - (-4)^2 = 14
\]
\[
12 - 16 = 14
\]
\[
-4 \neq 14
\]
Therefore, \((2, -4)\) is also **not** a solution.

Since both ordered pairs are not solutions to the equation, the correct response is:

**Neither ordered pair is a solution.**