Question

Which ordered pairs are in the solution set of the system of linear inequalities?

y≤2x−5 ,y≥−4x+3

a) (5, -2), (3, -1), (4, 2)
b) (5, -2), (3, 1), (-4, 2)
c) (5, -2), (3, -1), (4, -3)
d) (5, -2), (3, 1), (4, 3)

Answer 1

The ordered pairs in the solution set of the system of linear inequalities are (5, -2), (3, -1), (4, 2).

Step-by-step explanation:

Let's solve this system of linear inequalities:

y ≤ 2x - 5

y ≥ -4x + 3

To find the solutions, we need to determine which ordered pairs satisfy both of these inequalities.

We can check each option:

a) (5, -2):

Substituting the values, we have: -2 ≤ 2(5) - 5 and -2 ≥ -4(5) + 3

Both inequalities are true, so this ordered pair is in the solution set.

b) (5, -2):

Substituting the values, we have: -2 ≤ 2(3) - 5 and -2 ≥ -4(3) + 3

Both inequalities are true, so this ordered pair is in the solution set.

c) (5, -2):

Substituting the values, we have: -2 ≤ 2(4) - 5 and -2 ≥ -4(4) + 3

Both inequalities are true, so this ordered pair is in the solution set.

d) (5, -2):

Substituting the values, we have: -2 ≤ 2(5) - 5 and -2 ≥ -4(5) + 3

One inequality is true and the other is false. Therefore, this ordered pair is not in the solution set.

Based on our analysis, the a) (5, -2), (3, -1), (4, 2) ordered pairs are in the solution set of the system of linear inequalities.