Question

Determine whether the point (4,2) is in the solution set of the system of inequalities below:

4x + y ≤ 2

Which of the following points is in the solution set?

a. (3, 6)
b. (3, -2)
c. (3, -6)
d. (-3, 2)

Answer 1

The point (4,2) is not in the solution set of the inequality 4x + y ≤ 2, and the point (-3, 2) is in the solution set.

Step-by-step explanation:

To determine whether the point (4,2) is in the solution set of the system of inequalities, we substitute the values of x and y into the inequality and check if it is satisfied.

For the inequality 4x + y ≤ 2, let's substitute x = 4 and y = 2:

4(4) + (2) ≤ 2
16 + 2 ≤ 2
18 ≤ 2

The inequality 18 is not true, so the point (4,2) is not in the solution set.

Out of the given options, the only point that is in the solution set is d. (-3, 2).