Question

Which of the following points is a possible solution to the inequality 2x-3y<6?
Select all that would work.

(1,2)
(6,2)
(4,5)
(0,0)

Answer 1

To determine which points are possible solutions to the inequality 2x-3y<6, we need to substitute the x and y values into the inequality and check whether the inequality holds true.

Let's check each point:

1. (1,2)
Substituting the coordinates into the inequality:
2(1) - 3(2) < 6
2 - 6 < 6
-4 < 6

The inequality holds true for this point.

2. (6,2)
Substituting the coordinates into the inequality:
2(6) - 3(2) < 6
12 - 6 < 6
6 < 6

The inequality does not hold true for this point.

3. (4,5)
Substituting the coordinates into the inequality:
2(4) - 3(5) < 6
8 - 15 < 6
-7 < 6

The inequality holds true for this point.

4. (0,0)
Substituting the coordinates into the inequality:
2(0) - 3(0) < 6
0 - 0 < 6
0 < 6

The inequality holds true for this point.

Therefore, the possible solutions are (1,2), (4,5), and (0,0).