Answer
$(x,0)$ for $x\geq 0$
$(0,y)$ for $y\leq 0$
Work Step by Step
We are given the equation:
$|x+y|=x-y$
Case 1: $x\leq 0,y\leq 0$
$-(x+y)=x-y$
$-x-y=x-y$
$2x=0$
$x=0$
Solutions: $(0,y)$, where $y\leq 0$
Case 2: $x\geq 0,y\geq 0$
$x+y=x-y$
$2y=0$
$y=0$
Solutions: $(x,0)$, where $x\geq 0$
Case 3: $x\geq 0, y\leq 0$ and $|x|>|y|$
$x+y=x-y$
$2y=0$
$y=0$
Solutions: $(x,0)$, where $x\geq 0$
Case 4: $x\geq 0, y\leq 0$ and $|x||y|$
$-(x+y)=x-y$
$-x-y=x-y$
$2x=0$
$x=0$
No solution
Case 6: $x\leq 0, y\geq 0$ and $|x|
