Which of the following is a solution to the following system of inequalities?

solid line at y equals negative x plus one, dotted line at y equals two x plus 3, shaded above the first line and below the second line

(1, -1)

(-4, 0)

(3, -2)

(0, 3)

Option D: is the solution to the inequalities.

Explanation:

From the given graph, we can see that the equation of the inequalities are

and

To determine the coordinate that satisfies the inequality, let us substitute the coordinates in both of the inequalities and

Thus, we have,

Option A:

Substituting the coordinates in and , we get,

is not true.

is true.

Since, only one equation satisfies the condition, the coordinate is not a solution.

Hence, Option A is not the correct answer.

Option B:

Substituting the coordinates in and , we get,

is not true.

is not true.

Since, both the equations does not satisfy the condition, the coordinate is not a solution.

Hence, Option B is not the correct answer.

Option C:

Substituting the coordinates in and , we get,

is not true.

is true.

Since, only one equation satisfies the condition, the coordinate is not a solution.

Hence, Option C is not the correct answer.

Option D:

Substituting the coordinates in and , we get,

is true.

is true.

Since, both equation satisfies the condition, the coordinate is a solution.

Hence, Option D is the correct answer.

answer: both chords and diameters have two endpoints on a circle. diameters must intersect the center of a circle.