To determine which ordered pairs are solutions to the inequality x + 3y ≥ -8, we need to substitute the x and y values from each ordered pair into the inequality and check if the inequality holds true.
Let's go through each ordered pair one by one:
1) For the ordered pair (1, -1):
Substituting x = 1 and y = -1 into the inequality:
1 + 3(-1) ≥ -8
1 - 3 ≥ -8
-2 ≥ -8
Since -2 is indeed greater than or equal to -8, the ordered pair (1, -1) is a solution to the inequality.
2) For the ordered pair (0, -2):
Substituting x = 0 and y = -2 into the inequality:
0 + 3(-2) ≥ -8
0 - 6 ≥ -8
-6 ≥ -8
Again, -6 is greater than or equal to -8, so the ordered pair (0, -2) is a solution.
3) For the ordered pair (7, 12):
Substituting x = 7 and y = 12 into the inequality:
7 + 3(12) ≥ -8
7 + 36 ≥ -8
43 ≥ -8
Once more, 43 is greater than or equal to -8, so the ordered pair (7, 12) is a solution.
4) For the ordered pair (5, -3):
Substituting x = 5 and y = -3 into the inequality:
5 + 3(-3) ≥ -8
5 - 9 ≥ -8
-4 ≥ -8
As -4 is greater than or equal to -8, the ordered pair (5, -3) is a solution.
5) Lastly, for the ordered pair (-6, -3):
Substituting x = -6 and y = -3 into the inequality:
-6 + 3(-3) ≥ -8
-6 - 9 ≥ -8
-15 ≥ -8
Here, -15 is not greater than or equal to -8, so the ordered pair (-6, -3) is not a solution.
To summarize, the ordered pairs (1, -1), (0, -2), (7, 12), and (5, -3) are solutions to the inequality x + 3y ≥ -8. The ordered pair (-6, -3) is not a solution.