Which ordered pair is a solution to the system of inequalities?

y > 2x y >7
Solution:
Answer;
# (3,7)
A (0, 0)
$ (1,9)
(4,8)

1 answer

To determine which ordered pair is a solution to the system of inequalities \( y > 2x \) and \( y > 7 \), we can test each given ordered pair by plugging in the values into the inequalities.

  1. (3, 7):

    • For \( y > 2x \): \( 7 > 2(3) \) → \( 7 > 6 \) (True)
    • For \( y > 7 \): \( 7 > 7 \) (False)
  2. (0, 0):

    • For \( y > 2x \): \( 0 > 2(0) \) → \( 0 > 0 \) (False)
    • For \( y > 7 \): \( 0 > 7 \) (False)
  3. (1, 9):

    • For \( y > 2x \): \( 9 > 2(1) \) → \( 9 > 2 \) (True)
    • For \( y > 7 \): \( 9 > 7 \) (True)
  4. (4, 8):

    • For \( y > 2x \): \( 8 > 2(4) \) → \( 8 > 8 \) (False)
    • For \( y > 7 \): \( 8 > 7 \) (True)

Based on the above evaluations, the only ordered pair that satisfies both inequalities is (1, 9).

Thus, the answer is: (1, 9)