To solve the problem of finding the value of [tex]\( x \)[/tex] when [tex]\( y = 1 \)[/tex] given that [tex]\( x \)[/tex] varies inversely with [tex]\( y \)[/tex] and [tex]\( x \cdot y = 2 \)[/tex], follow these steps:
1. Understand the given equation [tex]\( x \cdot y = 2 \)[/tex]:
This equation tells us that the product of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] is a constant value, which is 2.
2. Substitute the given value [tex]\( y = 1 \)[/tex] into the equation:
Plug [tex]\( y = 1 \)[/tex] into the equation [tex]\( x \cdot y = 2 \)[/tex].
[tex]\[
x \cdot 1 = 2
\][/tex]
3. Simplify the equation:
Now, simplify this equation to find the value of [tex]\( x \)[/tex]:
[tex]\[
x = 2
\][/tex]
4. Conclusion:
After substituting and simplifying, we find that [tex]\( x = 2 \)[/tex].
Therefore, the value of [tex]\( x \)[/tex] when [tex]\( y = 1 \)[/tex] is [tex]\( \boxed{2} \)[/tex].
