Is xy > 0?
x - y > -2 and x - 2y < -6

Solution:

Removing the inequalities of the above two equations and solving for x and y we have the following

x - y = 2 --- (1)

x - 2y = 6 --- (2)

0 + y = -4

y = -4 --- (3)

Substituting y in equation (1)

x - (-4) = 2

x + 4 = 2

x = 2 - 4 = -2

x = -2

xy = (2/3)(-2) = -4/3

The product xy = - 4/3 is < 0 and NOT greater than zero

Is xy > 0?
x - y > -2 and x - 2y < -6

Summary:

The product xy is less than 0 and Not greater than zero for the given equations x - y > -2 and x - 2y < -6.