For the first inequality, (-1, -1) is the solution. For the second inequality, (1, -1) is the solution.
Inequality 1: 2x + y > -4
To determine which point is a solution to the inequality, substitute the coordinates of each point into the inequality and evaluate:
For point (0, -5):
2(0) + (-5) > -4 → -5 > -4
This statement is false, so (0, -5) is not a solution.
For point (4, -12):
2(4) + (-12) > -4 → -4 > -4
This statement is false, so (4, -12) is not a solution.
For point (-1, -1):
2(-1) + (-1) > -4 → -3 > -4
This statement is true, so (-1, -1) is a solution.
For point (-3, 0):
2(-3) + 0 > -4 → -6 > -4
This statement is false, so (-3, 0) is not a solution.
Therefore, the solution to the inequality 2x + y > -4 is (-1, -1).
Inequality 2: y - 2x ≤ -3
For point (2, 4):
4 - 2(2) ≤ -3 → 0 ≤ -3
This statement is false, so (2, 4) is not a solution.
For point (1, -1):
-1 - 2(1) ≤ -3 → -3 ≤ -3
This statement is true, so (1, -1) is a solution.
For point (3, 4):
4 - 2(3) ≤ -3 → -2 ≤ -3
This statement is false, so (3, 4) is not a solution.
For point (-2, 3):
3 - 2(-2) ≤ -3 → 7 ≤ -3
This statement is false, so (-2, 3) is not a solution.
Therefore, the solution to the inequality y - 2x ≤ -3 is (1, -1).