Question

Which of the following points is a possible solution to the inequality 2x−3y<6

?

Select all that would work.

(2 points)
Responses

(0,0)
open paren 0 comma 0 close paren

(1,2)
open paren 1 comma 2 close paren

(6,2)
open paren 6 comma 2 close paren

(4,5)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine which points are possible solutions to the inequality 2x - 3y < 6, we need to substitute the coordinates of each point into the inequality and check if the inequality is true or false.

For the given options:

1. (0,0):
2(0) - 3(0) < 6
0 < 6
This is true, so (0,0) is a possible solution.

2. (1,2):
2(1) - 3(2) < 6
2 - 6 < 6
-4 < 6
This is true, so (1,2) is a possible solution.

3. (6,2):
2(6) - 3(2) < 6
12 - 6 < 6
6 < 6
This is false, so (6,2) is not a possible solution.

4. (4,5):
2(4) - 3(5) < 6
8 - 15 < 6
-7 < 6
This is true, so (4,5) is a possible solution.

Therefore, the possible solutions to the inequality 2x - 3y < 6 are (0,0), (1,2), and (4,5).