QuestionTwo numbers, $x$ and $y$, are reciprocals. Which expression is always true? A. $xy=1$ B. $x-y=0$ C. $\frac{x}{y}=1$ D. $x+y=-1$ E. $x^{y}=1$

Studdy Solution
Now, let's compare this expression with the given options.
Option A $x \cdot y =1$ is exactly the definition of reciprocals. So, this expression is always true when $x$ and $y$ are reciprocals.
Option B $x - y =0$ implies $x = y$, which is not necessarily true for reciprocals. For example, if $x =2$ and $y =1/2$, they are reciprocals, but $x$ is not equal to $y$.
Option C $\frac{x}{y} =1$ implies $x = y$, which is not necessarily true for reciprocals, as explained in the previous step.
Option D $x + y = -1$ is not necessarily true for reciprocals. For example, if $x =2$ and $y =1/2$, they are reciprocals, but $x + y$ is not equal to $-1$.
Option $x^{y} =1$ is not necessarily true for reciprocals. For example, if $x =2$ and $y =1/2$, they are reciprocals, but $x^{y}$ is not equal to $1$.
Therefore, the expression that is always true when $x$ and $y$ are reciprocals is Option A $x \cdot y =1$.