According to my answer it's graph would be $x=y$ when $x,y\ge0$ and the whole third quadrant including $x=0$ and $y=0$, when $y$ is not a function of $x$. When it is a function of $x$ then the graph is $x=y$ when $x,y\ge0$ and the negative $x$-axis. According to a graphing utility (like Desmos) my answer is wrong. Please can someone correct me? I would be thankful.
Explain how can we graph the equation $y+|y|=x+|x|$.( Relation involving absolute values)
absolute valuealgebra-precalculusgraphing-functionsrelations
Best Answer
Without thinking too much :), just look exhaustively
at all 4 possible cases and see what they give you.
1) $x \ge 0, y \ge 0$ Then obviously you get $2y = 2x$ and then $y=x$
This when plotted is a ray: the bisector of 1st quadrant.
2) $x \ge 0, y \le 0$ Then you get $x = 0$ So any pair $(0, y \le 0)$ is a solution here.
3) $x \le 0, y \le 0$
Here you get $0=0$ which is always true.
So any pair $(x \le 0, y \le 0)$ is a solution.
4) $x \le 0, y \ge 0$
Then you get $y = 0$
So any pair $(x \le 0, 0)$ is a solution here.
So eventually you get this plot below
/ or maybe a slightly better one because I am bad painter :) /.
Final answer:
All points from 3rd quadrant, the contour of 3rd quadrant,
and the bisector of 1st quadrant. This is the graph of your
equation.
If some software gives you a different thing - don't trust it :)