Question

which ordered pair is a soulution to the equation. y=5x^2-2. (1, 5) (-1, 43) (-1, 5) (-1, 3)

Answer 1

To determine which ordered pair is a solution to the equation \( y = 5x^2 - 2 \), we can substitute the \( x \) value from each ordered pair into the equation and see if it gives the corresponding \( y \) value.

1. **For the pair (1, 5):**
\[
y = 5(1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3
\]
This does not equal 5, so (1, 5) is not a solution.

2. **For the pair (-1, 43):**
\[
y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3
\]
This does not equal 43, so (-1, 43) is not a solution.

3. **For the pair (-1, 5):**
\[
y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3
\]
This does not equal 5, so (-1, 5) is not a solution.

4. **For the pair (-1, 3):**
\[
y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3
\]
This equals 3, so (-1, 3) is a solution.

The only ordered pair that is a solution to the equation \( y = 5x^2 - 2 \) is **(-1, 3)**.