On the coordinate plane, plot all points whose coordinates are solutions to the equation: $y^{2}-|y|$ $=x^{2}-|x|$.
$y^{2}-|y|=x^{2}-|x| \Leftrightarrow y^{2}-x^{2}=|y|-|x| \Leftrightarrow(|y|-|x|)(|y|+|x|)=|y|-|x| \Leftrightarrow(|y|-|x|)(|y|+|x|-1)=0 \Leftrightarrow|y|+|x|=$ 1 or $|y|=|x|$.

## Answer

![](https://cdn.mathpix.com/cropped/2024_05_06_5008c33ea747074d348fg-10.jpg?height=257&width=240&top_left_y=1518&top_left_x=909)