Question
Which of the following ordered pairs is part of the solution set for the equation. Y = 5x^2 - 2?
1. (1, 5)
2. (-1, 3)
3. (-1, 43)
4. (-1, 5)
1. (1, 5)
2. (-1, 3)
3. (-1, 43)
4. (-1, 5)
Answers
GPT-4o mini
To determine which of the given ordered pairs is part of the solution set for the equation \( y = 5x^2 - 2 \), we will substitute the \( x \) values from each ordered pair into the equation and check if the corresponding \( y \) value matches.
1. For \( (1, 5) \):
\[
y = 5(1)^2 - 2 = 5 \cdot 1 - 2 = 5 - 2 = 3
\]
This gives \( (1, 3) \), not \( (1, 5) \). So this pair is **not** a solution.
2. For \( (-1, 3) \):
\[
y = 5(-1)^2 - 2 = 5 \cdot 1 - 2 = 5 - 2 = 3
\]
This gives \( (-1, 3) \). So this pair **is** a solution.
3. For \( (-1, 43) \):
Using the same calculation as above for \( x = -1 \):
\[
y = 3
\]
This does not match \( (-1, 43) \). So this pair is **not** a solution.
4. For \( (-1, 5) \):
Again using the calculation for \( x = -1 \):
\[
y = 3
\]
This does not match \( (-1, 5) \). So this pair is **not** a solution.
Thus, the only ordered pair that is part of the solution set for the equation \( y = 5x^2 - 2 \) is:
**2. (-1, 3)**.
1. For \( (1, 5) \):
\[
y = 5(1)^2 - 2 = 5 \cdot 1 - 2 = 5 - 2 = 3
\]
This gives \( (1, 3) \), not \( (1, 5) \). So this pair is **not** a solution.
2. For \( (-1, 3) \):
\[
y = 5(-1)^2 - 2 = 5 \cdot 1 - 2 = 5 - 2 = 3
\]
This gives \( (-1, 3) \). So this pair **is** a solution.
3. For \( (-1, 43) \):
Using the same calculation as above for \( x = -1 \):
\[
y = 3
\]
This does not match \( (-1, 43) \). So this pair is **not** a solution.
4. For \( (-1, 5) \):
Again using the calculation for \( x = -1 \):
\[
y = 3
\]
This does not match \( (-1, 5) \). So this pair is **not** a solution.
Thus, the only ordered pair that is part of the solution set for the equation \( y = 5x^2 - 2 \) is:
**2. (-1, 3)**.