Question

Determine which of the following ordered pairs is a solution to the equation 8−2y=4x^2 . Option #1: (0,8) Option #2: (−1,2) Option #3: (4,0) (1 point) Option # is a solution to the equation.

Answer 1

To determine which ordered pairs are solutions to the equation \( 8 - 2y = 4x^2 \), we'll substitute each pair into the equation and see if they satisfy it.

1. For Option #1: \( (0, 8) \)
- Substitute \( x = 0 \) and \( y = 8 \):
\[
8 - 2(8) = 4(0^2)
\]
\[
8 - 16 = 0
\]
\[
-8 \neq 0
\]
So, Option #1 is **not** a solution.

2. For Option #2: \( (-1, 2) \)
- Substitute \( x = -1 \) and \( y = 2 \):
\[
8 - 2(2) = 4(-1^2)
\]
\[
8 - 4 = 4(1)
\]
\[
4 = 4
\]
So, Option #2 **is** a solution.

3. For Option #3: \( (4, 0) \)
- Substitute \( x = 4 \) and \( y = 0 \):
\[
8 - 2(0) = 4(4^2)
\]
\[
8 = 4(16)
\]
\[
8 = 64
\]
So, Option #3 is **not** a solution.

Based on the calculations above, the ordered pair that is a solution to the equation is **Option #2: (-1, 2)**.