Question

Determine whether the points (–3,–2) and (3,2) are in the solution set of the system of inequalities below:

y ≤ ½x + 2
y < –2x – 3
Which of the following is true?
A) The point (–3,–2) is in the solution set, and the point (3,2) is not in the solution set.
B) Both points are in the solution set.
C) The point (–3,–2) is not in the solution set, and the point (3,2) is in the solution set.
D) Neither of the points is in the solution set.

Answer 1

The point (-3, -2) is not in the solution set and the point (3, 2) is in the solution set of the given system of inequalities.

Step-by-step explanation:

To determine whether the points (–3,–2) and (3,2) are in the solution set of the system of inequalities, we need to substitute the x and y values of these points into the inequalities and check if they satisfy the conditions.

For the first inequality, y ≤ ½x + 2, substituting (-3, -2) gives us -2 ≤ ½(-3) + 2, which simplifies to -2 ≤ -1. Since this is not true, the point (-3, -2) is not in the solution set of the first inequality.

For the second inequality, 2y < –2x – 3, substituting (3, 2) gives us 2(2) < –2(3) – 3, which simplifies to 4 < -6 - 3. Since this is not true, the point (3, 2) is also not in the solution set of the second inequality.

Therefore, option C) The point (–3,–2) is not in the solution set, and the point (3,2) is in the solution set.