How to find $x+y$ of this?

Question

$$|x.y| = -2x$$ $$|\frac{y}{x}| = 3y$$ So how do i find to $x+y$? I don't have any idea about the problem because it seems so hard to me. But I've tried a few ways to solve it and got $\frac{3}{2}$. I think I'm wrong.

Answer 1

From the first one, you get $$ |y| = \frac{-2x}{|x|}, $$ and since LHS is non-negative, we must have $x \le 0$, which yields $|y| = 2$.

From the second one, $$ |x| = \frac{|y|}{3y}, $$ and since LHS is non-negative, $y \ge 0$, which implies $y=2$. That means, $x=-1/3$.

Answer 2

The absolute values are non-negative, so $-2x\geq0$ and $3y\geq0$. Apparently $x\neq0$ so that the second equation can make sense, so we get $x<0$ and $y\geq0$. Knowing this, the system becomes $$ \begin{cases} xy&=&2x\\ -y/x&=&3y. \end{cases} $$ Can you now solve $y$ from the first equation? After that you can get $x$ from the second one.