Question

Which of the following ordered pairs is part of the solution set for the equation: y = 5x^2 - 2
A. (1, 5)
B. (-1, 43)
C. (-1, 3)
D. (-1, 5)

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-value from each ordered pair into the equation and see if it produces the corresponding y-value.

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

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

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

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

The only ordered pair that is part of the solution set for the equation \( y = 5x^2 - 2 \) is **C. (-1, 3)**.