Question

given \\(x\\) varies inversely with \\(y\\) and \\(xy = 2\\), what is the value of \\(x\\) when \\(y = 1\\)?

\\(\bigcirc\\) -1

\\(\bigcirc\\) \\(\frac{1}{2}\\)

\\(\bigcirc\\) 1

\\(\bigcirc\\) 2

Explanation:

🆕 New Concept Discovered: Inverse Variation
Two quantities change in opposite directions

Step 1: Identify the relationship

When two variables \(x\) and \(y\) vary inversely, their product is always equal to a constant value \(k\):

$$xy = k$$

We are given the equation:

$$xy = 2$$

This means the constant of variation is \(k = 2\).

Step 2: Substitute the given value

To find the value of \(x\) when \(y = 1\), substitute \(y = 1\) into the equation:

$$x(1) = 2$$

Step 3: Solve for x

$$x = 2$$

Answer:

2