Question

Which ordered pair is in the solution set of 2x – 3y < 6?

Option 1: (-2, 2)
Option 2: (0, -3)
Option 3: (3, 1)
Option 4: (-1, -1)

Answer 1

To determine which ordered pair is in the solution set of 2x - 3y < 6, we substitute the values of x and y from each option into the inequality and see which produces a true statement. The ordered pair (-2, 2) satisfies the inequality.

Step-by-step explanation:

To determine which ordered pair is in the solution set of the inequality 2x - 3y < 6, we need to substitute the values of x and y from each option into the inequality and see if the resulting inequality is true. Let's go through each option:

1. Option 1: (-2, 2)
   When x = -2 and y = 2:
   2(-2) - 3(2) = -4 - 6 = -10, which is less than 6. So, (-2, 2) satisfies the inequality.
2. Option 2: (0, -3)
   When x = 0 and y = -3:
   2(0) - 3(-3) = 0 + 9 = 9, which is not less than 6. So, (0, -3) does not satisfy the inequality.
3. Option 3: (3, 1)
   When x = 3 and y = 1:
   2(3) - 3(1) = 6 - 3 = 3, which is not less than 6. So, (3, 1) does not satisfy the inequality.
4. Option 4: (-1, -1)
   When x = -1 and y = -1:
   2(-1) - 3(-1) = -2 + 3 = 1, which is not less than 6. So, (-1, -1) does not satisfy the inequality.

Therefore, the ordered pair that is in the solution set of 2x - 3y < 6 is Option 1: (-2, 2).