Question

State if the given ordered pairs are solutions to the given systems of inequalities or the graph o

the system of inequalities.

a. (0,-5)
b. (4,1)
c. (6, 1)
d. (1,-6)

Answer 1

The ordered pairs in the solution to the systems of inequalities are (0, -5) and (6, 1)

Solving the systems of inequalities graphically

From the question, we have the following parameters that can be used in our computation:

The system of inequalities represented by the graph

From the given graph, we have solution to the system to be the shaded region

This means that all coordinates in the shaded region are the solutions to the system

Using the above as a guide, we have the following:

The coordinates in the shaded region are (0, -5) and (6, 1)

Answer 2

a) Solution

b) Not a solution

c) Solution

d) Not a solution

Explanation:

The solutions to a graphed system of inequalities are found in the region where the shaded areas of the individual inequalities overlap. Points located on a solid boundary line are included in the solution, whereas points located on a dashed boundary line are not included in the solution.

a) Point (0, -5)

Point (0, -5) lies precisely on the solid boundary line of one of the inequalities. As points on solid boundary lines are included in the solution, point (0, -5) is a valid solution to the given system of inequalities.

b) Point (4, 1)

Point (4, 1) is positioned on the dashed boundary line of one of the inequalities. Since points on dashed boundary lines are not included in the solution, point (4, 1) is not a valid solution to the given system of inequalities.

c) Point (6, 1)

As point (6, 1) is located inside the overlapping shaded region, it is a valid solution to the given systems of inequalities.

d) Point (1, -6)

As point (1, -6) is located outside the overlapping shaded region, it is a not a valid solution to the given systems of inequalities.