Question

Determine which of the following ordered pairs is a solution to the equation 8−2y=4x2 .

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 of the given ordered pairs is a solution to the equation \( 8 - 2y = 4x^2 \), we will substitute each pair into the equation and check if it holds true.

1. **Option #1: (0, 8)**
\[
x = 0, \quad y = 8
\]
Substitute into the equation:
\[
8 - 2(8) = 4(0)^2
\]
Simplifying the left side:
\[
8 - 16 = 0
\]
\[
-8 \neq 0
\]
This pair is **not** a solution.

2. **Option #2: (-1, 2)**
\[
x = -1, \quad y = 2
\]
Substitute into the equation:
\[
8 - 2(2) = 4(-1)^2
\]
Simplifying the left side:
\[
8 - 4 = 4
\]
\[
4 = 4
\]
This pair **is** a solution.

3. **Option #3: (4, 0)**
\[
x = 4, \quad y = 0
\]
Substitute into the equation:
\[
8 - 2(0) = 4(4)^2
\]
Simplifying the left side:
\[
8 - 0 = 4(16)
\]
\[
8 = 64
\]
This pair is **not** a solution.

Hence, the correct answer is:

**Option #2: (-1, 2) is a solution to the equation.**