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AlgebraHardPoint satisfying a system of inequalities

Algebra practice question

Which point (x, y) satisfies both y > 2x − 3 and y ≤ −x + 6?

  1. A. (1, 4)Correct
  2. B. (3, 1)
  3. C. (1, 6)
  4. D. (4, 0)

Answer: A. (1, 4)

At (1, 4): 4 > 2(1) − 3 = −1 holds, and 4 ≤ −1 + 6 = 5 holds.

Why the other answers are wrong

B. (3, 1)
(3, 1): the first inequality needs y > 3, but y = 1.
C. (1, 6)
(1, 6): the second inequality caps y at 5, but y = 6.
D. (4, 0)
(4, 0): the first inequality needs y > 5, but y = 0.

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