16Hit1600
AlgebraVery hardOrdered pair satisfying two inequalities

Algebra practice question

y ≥ x + 1 y ≤ 2x − 3

Which ordered pair (x, y) satisfies both inequalities?

  1. A. (5, 7)Correct
  2. B. (2, 3)
  3. C. (4, 4)
  4. D. (6, 10)

Answer: A. (5, 7)

Test (5, 7): 7 ≥ 5 + 1 = 6 is true, and 7 ≤ 2(5) − 3 = 7 is true (equality counts for ≤). Both hold.

Why the other answers are wrong

B. (2, 3)
(2, 3) passes the first (3 ≥ 3) but fails the second: 3 ≤ 2(2) − 3 = 1 is false.
C. (4, 4)
(4, 4) fails the first: 4 ≥ 4 + 1 = 5 is false.
D. (6, 10)
(6, 10) passes the first (10 ≥ 7) but fails the second: 10 ≤ 2(6) − 3 = 9 is false.

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