Given [tex]x[/tex] varies inversely with [tex]y[/tex] and [tex]xy = 2[/tex], what is the value of [tex]x[/tex] when [tex]y = 1[/tex]?

A. [tex]-1[/tex]
B. [tex]\frac{1}{2}[/tex]
C. [tex]1[/tex]
D. [tex]2[/tex]



Answer :

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].