Question

Decide whether each point is a solution to the system. y ≤ +4 and y < 3x-2.

a. (0, -2)
b. (5, 0)
c. (3, 13)
d. None of the above

Answer 1

To decide whether each point is a solution to the system, plug in the x and y values of each point into the inequalities and check if the inequalities are true. Only point b. (5, 0) satisfies both inequalities.

Step-by-step explanation:

To decide whether each point is a solution to the system, we need to plug in the x and y values of each point into the inequalities and check if the inequalities are true. Let's evaluate each point:

a. (0, -2):

First inequality: -2 ≤ 4 + 4 = 8 (False)

Second inequality: -2 < 3(0) - 2 = -2 (True)

b. (5, 0):

First inequality: 0 ≤ 5 + 4 = 9 (False)

Second inequality: 0 < 3(5) - 2 = 13 (True)

c. (3, 13):

First inequality: 13 ≤ 3 + 4 = 7 (False)

Second inequality: 13 < 3(3) - 2 = 7 (False)

Based on these evaluations, only point b. (5, 0) satisfies both inequalities. Therefore, the correct answer is d. None of the above.