16Hit1600
AlgebraHardTesting a point against a system of inequalities

Algebra practice question

y > 2x − 1 y ≤ −x + 5

Which of the following points in the xy-plane is a solution to the system?

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

Answer: A. (1, 2)

A point is a solution only if it satisfies BOTH inequalities. Test (1, 2): 2 > 2(1) − 1 = 1 is true, and 2 ≤ −1 + 5 = 4 is true. So (1, 2) works.

Why the other answers are wrong

B. (3, 2)
(3, 2) fails the first inequality: 2 > 2(3) − 1 = 5 is false.
C. (0, 6)
(0, 6) passes the first (6 > −1) but fails the second: 6 ≤ 0 + 5 is false.
D. (2, 3)
(2, 3) gives 3 > 2(2) − 1 = 3, and 3 > 3 is false — the first inequality is strict, so equality doesn't count.

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