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📐 Mathematics  ·  Linear Inequalities  ·  JEE

The solution of the system 2x + y > 4 and x - y < 1 includes which of these points?

Answer: (2, 3).

  • A (2, 3)
  • B (0, 0)
  • C (1, 1)
  • D (-1, -1)

Correct answer: A. (2, 3)

Explanation: At (2,3): 2(2)+3 = 7 > 4 is true, and 2-3 = -1 < 1 is true, so both conditions hold. The other points all fail the first condition, since 2x+y is at most 3 for each of them.

Number Line vs Half-Plane Representationx > 2 (open circle, hollow)2x ≤ 2 (closed circle, filled)shaded regionsatisfies the inequality2D inequality: dashed line = strict, shaded = solution side

One-variable inequalities use open (excluded) or closed (included) circles on a number line; two-variable inequalities use a dashed (strict) or solid (non-strict) boundary line, with the solution being the entire shaded half-plane on one side of it.

Concept context

Solving linear inequalities in one and two variables algebraically and graphically, and representing solutions on a number line or as a region in a plane.

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