# Computing the product $xy$

$$\dfrac{|x|}{2}=y$$

$$|y|-x=4$$

• Compute $$xy$$

Here I would have been able to solve this question in such case there was only one unknown. I, however, cannot solve this type of questions when there are more than one unknown so let me at least share my thoughts with you.

$$|x| = 2y \implies \dfrac{1}{2}|x| = y$$

Plugging into the second equation and we get that

$$\biggr |\dfrac{1}{2}|x|\biggr |-x = 4$$

This is where I'm stuck.

Regards

Since $$y=|x|/2$$ you know $$y\ge 0,$$ so in the second equation $$|y|$$ can be replaced by simply $$y.$$
Hint: Since $$y=|x|/2\implies y\geq 0\implies |y|=y$$
so $$|x|= 2(x+4)\implies ...$$
$$y=|x|/2\implies y\geq 0\implies |y|=y$$ Also $$|x|=2y, |y|-x=y-x=4$$ If $$x$$ is positive, then $$x=2y$$ $$y-x=y-2y=-y=4\implies y=-4$$ which contradicts the claim that $$y \geq 0$$ So $$x\le0$$, and $$x=-2y$$ $$y-x=y-(-2y)=3y=4\implies y=4/3$$ $$x=-2y=-8/3$$ $$xy=-32/9$$
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