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

### Check Option #1: \((0, 8)\)
Substituting \(x = 0\) and \(y = 8\) into the equation:
\[
8 - 2(8) = 4(0^2)
\]
\[
8 - 16 = 0
\]
\[
-8 = 0 \quad \text{(False)}
\]

### Check Option #2: \((-1, 2)\)
Substituting \(x = -1\) and \(y = 2\) into the equation:
\[
8 - 2(2) = 4(-1^2)
\]
\[
8 - 4 = 4(1)
\]
\[
4 = 4 \quad \text{(True)}
\]

### Check Option #3: \((4, 0)\)
Substituting \(x = 4\) and \(y = 0\) into the equation:
\[
8 - 2(0) = 4(4^2)
\]
\[
8 = 4(16)
\]
\[
8 = 64 \quad \text{(False)}
\]

The only ordered pair that is a solution to the equation is **Option #2: (-1, 2)**.

So, Option #2 is a solution to the equation.