Question
Which of the following ordered pairs is part of the solution set for the equation y = 5x ^ 2 - 2
(- 1, 5)
(- 1, 43)
(- 1, 3)
(1, 5)
(- 1, 5)
(- 1, 43)
(- 1, 3)
(1, 5)
Answers
GPT-4o mini
To determine which of the ordered pairs is part of the solution set for the equation \( y = 5x^2 - 2 \), we will substitute the \( x \) value of each ordered pair into the equation and check if the resulting \( y \) value matches the \( y \) value in the ordered pair.
1. For the pair \((-1, 5)\):
\[
y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3
\]
The calculated \( y \) is 3, which does not match 5. Therefore, \((-1, 5)\) is **not** a solution.
2. For the pair \((-1, 43)\):
\[
y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3
\]
The calculated \( y \) is 3, which does not match 43. Therefore, \((-1, 43)\) is **not** a solution.
3. For the pair \((-1, 3)\):
\[
y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3
\]
The calculated \( y \) is 3, which matches 3. Therefore, \((-1, 3)\) **is** a solution.
4. For the pair \((1, 5)\):
\[
y = 5(1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3
\]
The calculated \( y \) is 3, which does not match 5. Therefore, \((1, 5)\) is **not** a solution.
Based on the calculations, the only ordered pair that is part of the solution set is \((-1, 3)\).
1. For the pair \((-1, 5)\):
\[
y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3
\]
The calculated \( y \) is 3, which does not match 5. Therefore, \((-1, 5)\) is **not** a solution.
2. For the pair \((-1, 43)\):
\[
y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3
\]
The calculated \( y \) is 3, which does not match 43. Therefore, \((-1, 43)\) is **not** a solution.
3. For the pair \((-1, 3)\):
\[
y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3
\]
The calculated \( y \) is 3, which matches 3. Therefore, \((-1, 3)\) **is** a solution.
4. For the pair \((1, 5)\):
\[
y = 5(1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3
\]
The calculated \( y \) is 3, which does not match 5. Therefore, \((1, 5)\) is **not** a solution.
Based on the calculations, the only ordered pair that is part of the solution set is \((-1, 3)\).