Isolating y² in the equation 4x² + 25y² = 100, by subtracting 4x² from both sides and dividing the whole by 25, we get y² = 4 - (4/25)x².
How do you isolate a variable in an equation?
To isolate a variable, start by "doing something to both sides" of the equation, such as adding, subtracting, multiplying, or dividing both sides of the equation by the same value. We may isolate the variable on one side of the equation by repeating this technique.
How do we solve the given question?
We are asked to isolate y² in the equation: 4x² + 25y² = 100.
To isolate y², we do the following steps:
Step 1: Subtracting 4x² from both sides of the equation.
4x² + 25y² - 4x² = 100 - 4x².
⇒ 25y² = 100 - 4x² (Simplifying)
Step 2: Divide both sides of the equation by 25.
25y²/25 = (100 - 4x²)/25
⇒ y² = 4 - (4/25)x². (Simplifying)
∴ Isolating y² in the equation 4x² + 25y² = 100, we get:
y² = 4 - (4/25)x².
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