Questions: UNIT 6 LESSON 2 2-Variable Equations Inequalities Equations in Two Variables Back to Intro Page Equations in Two Variables Practice complete this assessment to review what you've learned. It will not count toward your grade. Determine which of the following ordered pairs is a solution to the equation Item 1 8-2y=4x^2. Option #1: (0,8) Option #2: (-1,2) Option #3: (4,0) Option # is a solution to the equation.

UNIT 6 LESSON 2 2-Variable Equations Inequalities Equations in Two Variables Back to Intro Page Equations in Two Variables Practice complete this assessment to review what you've learned. It will not count toward your grade. Determine which of the following ordered pairs is a solution to the equation Item 1 8-2y=4x^2. Option #1: (0,8) Option #2: (-1,2) Option #3: (4,0) Option # is a solution to the equation.
Transcript text: UNIT 6 LESSON 2 2-Variable Equations \& Inequalities Equations in Two Variables Back to Intro Page Equations in Two Variables Practice complete this assessment to review what you've learned. It will not count toward your grade. Determine which of the following ordered pairs is a solution to the equation Item 1 $8-2 y=4 x^{2}$. Item 2 Option \#1: $(0,8)$ Item 3 Option \#2: $(-1,2)$ Option \#3: $(4,0)$ Item 4 (1 point) Item 5 Option \# $\square$ is a solution to the equation. Check answer Remaining Attempts : 3
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Solution

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Solution Steps

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

Solution Approach
  1. Substitute each ordered pair \((x, y)\) into the equation \(8 - 2y = 4x^2\).
  2. Check if the left-hand side equals the right-hand side for each pair.
  3. Identify the pair(s) that satisfy the equation.
Step 1: Substitute Ordered Pairs

We will substitute each ordered pair \((x, y)\) into the equation \(8 - 2y = 4x^2\) to check if they satisfy the equation.

Step 2: Check Option #1: \((0, 8)\)

Substituting \((0, 8)\): \[ 8 - 2(8) = 8 - 16 = -8 \quad \text{and} \quad 4(0)^2 = 0 \] Since \(-8 \neq 0\), option #1 is not a solution.

Step 3: Check Option #2: \((-1, 2)\)

Substituting \((-1, 2)\): \[ 8 - 2(2) = 8 - 4 = 4 \quad \text{and} \quad 4(-1)^2 = 4(1) = 4 \] Since \(4 = 4\), option #2 is a solution.

Step 4: Check Option #3: \((4, 0)\)

Substituting \((4, 0)\): \[ 8 - 2(0) = 8 - 0 = 8 \quad \text{and} \quad 4(4)^2 = 4(16) = 64 \] Since \(8 \neq 64\), option #3 is not a solution.

Final Answer

The only ordered pair that is a solution to the equation \(8 - 2y = 4x^2\) is option #2: \((-1, 2)\).

Thus, the answer is \(\boxed{(-1, 2)}\).

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