The system of inequalities D. The point (-9, 4) is not a solution of the system, but the point (-2, 4) is a solution of the system. Therefore , D. The point (-9, 4) is not a solution of the system, but the point (-2, 4) is a solution of the system is correct .
To check if a point is a solution of a system of inequalities, we need to substitute the coordinates of the point into each inequality and see if the inequality is satisfied.
First inequality: x+y>−2
Substituting (−9,4) into the inequality, we get:
-9 + 4 > -2
This is true, so the point (−9,4) satisfies the first inequality.
Second inequality: x−y<6
Substituting (−9,4) into the inequality, we get:
-9 - 4 < 6
This is also true, so the point (−9,4) satisfies the second inequality.
Therefore, the point (−9,4) is a solution of the system of inequalities.
The other answer choices are incorrect:
A: The point (−9,4) is a solution of the system of inequalities.
B: The point (−9,4) is not a solution of the system of inequalities. The point (−9,−3) is a solution of the system.
C: The point (−9,4) is not a solution of the system of inequalities. The point (−2,4) is a solution of the system.