Graphically, a point is a solution to a system of two inequalities if and only if __________.
(i) the point lies in the shaded region of the top inequality, but not in the shaded region of the bottom inequality
(ii) the point lies in the shaded region of the bottom inequality, but not in the shaded region of the top inequality
(iii) the point lies in the shaded regions of both the top and bottom inequalities
(iv) the point does not lie in the shaded regions of the top or bottom inequalities

Solution:

The answer is “the point lies in the shaded regions of both the top and bottom inequalities”

Consider equation x + y ⩽ 8 and x + y ⩽ 4, the graph is represented below. 

The shaded region represents the solution of the given set of inequalities. Take any point in the shaded region, say (4, 2), which satisfies both the inequalities and we may note that this is also the point that lies in both top and bottom regions of the inequalities.

Graphically, a point is a solution to a system of two inequalities if and only if __________.
(i) the point lies in the shaded region of the top inequality, but not in the shaded region of the bottom inequality
(ii) the point lies in the shaded region of the bottom inequality, but not in the shaded region of the top inequality
(iii) the point lies in the shaded regions of both the top and bottom inequalities
(iv) the point does not lie in the shaded regions of the top or bottom inequalities

Summary:

A point is a solution to a system of two inequalities if and only if the point lies in the shaded regions of both the top and bottom inequalities.