Questions: What is the result of isolating (y^2) in the equation below? [4 x^2+25 y^2=100] A. (y^2=100-4 x^2) B. (y^2=4-frac425 x^2) C. (y^2=100-frac425 x^2) D. (y^2=25-frac425 x^2)

What is the result of isolating (y^2) in the equation below? [4 x^2+25 y^2=100] A. (y^2=100-4 x^2) B. (y^2=4-frac425 x^2) C. (y^2=100-frac425 x^2) D. (y^2=25-frac425 x^2)
Transcript text: AA course.apeẋlearning.com Apex Leanning 4.2.3 Quiz: Nonlinear Systems of Equations Question 3 of 10 What is the result of isolating $y^{2}$ in the equation below? \[ 4 x^{2}+25 y^{2}=100 \] A. $y^{2}=100-4 x^{2}$ B. $y^{2}=4-\frac{4}{25} x^{2}$ C. $y^{2}=100-\frac{4}{25} x^{2}$ D. $y^{2}=25-\frac{4}{25} x^{2}$ PREVIOUS
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Solution

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Solution Steps

Step 1: Start with the given equation

The given equation is: \[ 4x^{2} + 25y^{2} = 100 \]

Step 2: Isolate the term containing \( y^{2} \)

Subtract \( 4x^{2} \) from both sides of the equation to isolate the term with \( y^{2} \): \[ 25y^{2} = 100 - 4x^{2} \]

Step 3: Solve for \( y^{2} \)

Divide both sides of the equation by 25 to solve for \( y^{2} \): \[ y^{2} = \frac{100 - 4x^{2}}{25} \]

Step 4: Simplify the equation

Simplify the right-hand side of the equation: \[ y^{2} = 4 - \frac{4}{25}x^{2} \]

Final Answer

The correct answer is B. \( y^{2} = 4 - \frac{4}{25}x^{2} \)

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