Question

On the coordinates plane XOY hatch a set of points whose coordinates satisfy the following inequalities in two variables x and y (show the boundary belonging to the set by a solid line and that not belonging to the set by a dash line).
$\frac{y-|x|}{x{y}^2}⩾0$

Answer 1

R.E.F image

$\frac{y-|x|}{x{y}^2}\ge 0$ $x\ne 0$ & $y\ne 0$

case (1) When $x>0\Rightarrow |x|=x$

$\frac{y-x}{x}\ge 0$

Since $x\ge 0\Rightarrow y\ge x$

$x\ne 0$ (y -axis is not including)

Case(2) When $x<0\Rightarrow |x|=-x$

$\frac{y+x}{-x}\ge 0$ since $\frac{x<0}{y+x\le 0}$

Now,

$y\le -x$

Now, we have to take union of both the cases

Points of shaded region & dark boundary will satisfy.