Question

Given the system of inequalities below:

-3x - y < 12

2x + 3y ≥ 9
Give the coordinates of three points that are members of the solution set.

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Answer 1

To find points in the solution set of the system of inequalities, we can solve each inequality separately. For the inequality -3x - y < 12, one possible point is (0, -11). For the inequality 2x + 3y ≥ 9, two possible points are (0, 3) and (4.5, 0).

Step-by-step explanation:

To find points that are members of the solution set, we can solve the system of inequalities. Let's start with the first inequality, -3x - y < 12:

1. Pick a value for x. For example, let x = 0.

2. Substitute the value of x into the inequality:

-3(0) - y < 12

-y < 12

y > -12

So when x = 0, y can be any value greater than -12. One possible point is (0, -11).

3. Repeat steps 1 and 2 to find two more points that are members of the solution set.

For the second inequality, 2x + 3y ≥ 9:

1. Let x = 0:

2(0) + 3y ≥ 9

3y ≥ 9

y ≥ 3

So when x = 0, y can be any value greater than or equal to 3. Another possible point is (0, 3).

2. Let y = 0:

2x + 3(0) ≥ 9

2x ≥ 9

x ≥ 4.5

So when y = 0, x can be any value greater than or equal to 4.5. One more possible point is (4.5, 0).