Question

Which of the following ordered pairs is in the feasible region for the following system of inequalities? 8x−y<5

a. (2, 0)
b. (1, 10)
c. (3, 25)
d. (4, 32)

Answer 1

To determine which ordered pairs are in the feasible region of the inequality 8x-y<5, we substitute the values of the pairs into the inequality. Options (b), (c), and (d) satisfy this inequality, but we would need all inequalities in the system to decisively determine the feasible region.

Step-by-step explanation:

To find which ordered pair is in the feasible region for the system of inequalities 8x-y<5, we must test each option by plugging the values of x and y into the inequality and checking if the inequality holds true.

1. For option (a) (2, 0), we test 8(2) - 0 < 5, which simplifies to 16 < 5. This is not true, so (a) is not in the feasible region.
2. For option (b) (1, 10), we test 8(1) - 10 < 5, which simplifies to -2 < 5. This is true, so (b) could be in the feasible region.
3. For option (c) (3, 25), we test 8(3) - 25 < 5, which simplifies to 24 - 25 < 5. This gives -1 < 5, which is true, so (c) could also be in the feasible region.
4. For option (d) (4, 32), we test 8(4) - 32 < 5, which simplifies to 32 - 32 < 5. This gives 0 < 5, which is true, so (d) could also be in the feasible region.

However, we must also consider that an ordered pair must satisfy all inequalities in the system. Given that there's only one inequality provided, we have three possible options. In practice, one would check the ordered pairs against all inequalities in the system to determine whether they are indeed in the feasible region.