Question

1. given that $x^{2}=y^{2}$, compare: a. $x$ b. $y$

Explanation:

Step1: Rearrange the given equation

$x^2 - y^2 = 0$

Step2: Factor the difference of squares

$(x-y)(x+y) = 0$

Step3: Analyze the solutions

This equation holds when $x=y$ OR $x=-y$. So $x$ could equal $y$, or $x$ could be the negative of $y$. For example, if $x=2$, $y$ could be 2 or -2; if $x=-3$, $y$ could be -3 or 3. This means we cannot definitively say $x$ is greater than, less than, or always equal to $y$.

Answer:

The relationship between $x$ and $y$ cannot be determined. $x$ may equal $y$, or $x$ may be the negative of $y$.