2. On the coordinate plane ( $x, y$ ), plot the set of all points for which $y^{2}-y=x^{2}-x$.

#
# Solution.

![](https://cdn.mathpix.com/cropped/2024_05_06_47d1c4c53e1180e4e9c9g-1.jpg?height=831&width=779&top_left_y=1201&top_left_x=407)

Solution. $y^{2}-y=x^{2}-x \Leftrightarrow y^{2}-x^{2}=y-x \Leftrightarrow (y-x)(y+x)=y-x \Leftrightarrow y=x$ or $y+x=1$