Question

Which of the following ordered pairs is part of the solution set for the equation y=5x2−2 ?

(1 point)
Responses

(1,5)
left parenthesis 1 comma 5 right parenthesis

(−1,43)
left parenthesis negative 1 comma 43 right parenthesis

(−1,5)
left parenthesis negative 1 comma 5 right parenthesis

(−1,3)

Answer 1

To determine which ordered pairs are part of the solution set for the equation \( y = 5x^2 - 2 \), we will substitute the \( x \) values from each pair into the equation and see if we get the corresponding \( y \) values.

1. **For the pair (1, 5):**
\[
y = 5(1^2) - 2 = 5(1) - 2 = 5 - 2 = 3
\]
The result is \( 3 \), not \( 5 \). So, (1, 5) is **not** a solution.

2. **For the pair (−1, 43):**
\[
y = 5(-1^2) - 2 = 5(1) - 2 = 5 - 2 = 3
\]
The result is \( 3 \), not \( 43 \). So, (−1, 43) is **not** a solution.

3. **For the pair (−1, 5):**
\[
y = 5(-1^2) - 2 = 5(1) - 2 = 5 - 2 = 3
\]
The result is \( 3 \), not \( 5 \). So, (−1, 5) is **not** a solution.

4. **For the pair (−1, 3):**
\[
y = 5(-1^2) - 2 = 5(1) - 2 = 5 - 2 = 3
\]
The result is \( 3 \), which matches the \( y \) value in the ordered pair. So, (−1, 3) is a solution.

Thus, the ordered pair that is part of the solution set for the equation is **(−1, 3)**.