Question

{x,y: |xy|<2}

Answer 1

since the signs of x and y do not count. consider the case x>0 and y>0. then add all other possible (x,y) thanks to symmetry.

xy < 2 <=> y<2/x., with y,x>0.

Answer 2

do you have to draw the set of solutions?

Answer 3

yes

Answer 4

can you graph it too plaease ?

Answer 5

I'll graph what I obtained.

the shaded is part of the solution because you can take all y such that 0<y<2/x given some x>0. see that it represents the region below the curve y=2/x ?

by symmetry, you will obtain the 4 other parts.