What is "given x varies inversely with y and xy = 2?

When two quantities vary inversely with each other, it means that as one quantity increases, the other quantity decreases in such a way that their product remains constant.

In this case, given that x varies inversely with y, we can write the relationship as:

x = k/y

where k is a constant of proportionality.

Additionally, we are given that the product of x and y is equal to 2:

xy = 2

Substitute the expression x = k/y into the equation xy = 2:

(k/y) * y = 2 k = 2

Therefore, the relationship between x and y is:

x = 2/y

This relationship shows that as y increases, x decreases in such a way that the product of x and y equals 2.