AlgebraVery hardOrdered pair satisfying two inequalities
Algebra practice question
y ≥ x + 1
y ≤ 2x − 3
Which ordered pair (x, y) satisfies both inequalities?
- A. (5, 7)Correct
- B. (2, 3)
- C. (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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