Question

Check all ordered pairs that are solutions to the following system of linear inequalities.

x + y > 5
y > 3 - 5
y < 5
2 < 8

A) (-8, 10)
B) (-14, 9)
C) (-11, 17)
D) (6, 2)

Answer 1

To find the ordered pairs that are solutions to the system of linear inequalities, we need to check each ordered pair and see if it satisfies all the inequalities. The ordered pair that satisfies all the inequalities is (6, 2).

Step-by-step explanation:

To find the ordered pairs that are solutions to the system of linear inequalities, we need to check each ordered pair and see if it satisfies all the inequalities.

1. For (-8, 10):
   a) x + y = -8 + 10 = 2 > 5, so this inequality is not satisfied.
   b) y = 10 > 3 - 5 = -2, so this inequality is satisfied.
   c) y = 10 < 5, so this inequality is not satisfied.
   d) 2 < 8, so this inequality is satisfied.
   This ordered pair does not satisfy all the inequalities.
2. Repeat the same process for the other ordered pairs and check if they satisfy all the inequalities.
3. Based on the checks, the only ordered pair that satisfies all the inequalities is D) (6, 2).