Question

A system of linear inequalities can have solutions in exactly three of the quadrants

Answer 1

It would be true that all three quadrants could be occupied

Answer 2

Answer with explanation:

Consider the Inequality

    x - y >0

⇒x > y

or, x -y < 0

⇒ x < y

It has solution in all the three regions.

Plotting the Inequality in x y plane and showing that the solution lies in three of the Quadrants

So, Yes , a system of linear inequalities can have solutions in exactly three of the quadrants.