Question

Identify two points that belong exclusively to the solution set of inequalities.

A. (0, 0) and (1, 1)
B. (-2, 3) and (4, 0)
C. (5, 2) and (-1, 1)
D. (0, 5) and (3, -2)

Answer 1

The two points that belong exclusively to the solution set of inequalities are (0, 5) and (3, -2).

Step-by-step explanation:

The two points that belong exclusively to the solution set of inequalities are option D. (0, 5) and (3, -2).

To identify these points, we need to substitute the x and y values of each point into the given inequalities. If the resulting values satisfy both inequalities, then the point belongs to the solution set.

For point (0, 5), we substitute x = 0 and y = 5 into the inequalities: x + y > 4 and 2x - y > -10. The resulting values are 5 > 4 and -5 > -10, which satisfy both inequalities.

Similarly, for point (3, -2), we substitute x = 3 and y = -2 into the inequalities: x + y > 4 and 2x - y > -10. The resulting values are 1 > 4 and 8 > -10, which satisfy both inequalities. Therefore, option D is correct.