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📐 Mathematics  ·  Linear Inequalities  ·  JEE

For what values of k does the system x + y <= k and x - y <= 2 (with x, y >= 0) have a feasible region that includes the point (3, 1)?

Answer: k >= 4.

  • A k >= 4
  • B k <= 4
  • C k >= 2
  • D k <= 2

Correct answer: A. k >= 4

Explanation: At (3,1): x+y=4 and x-y=2. For (3,1) to be feasible under x+y<=k, we need k >= 4 (the second constraint x-y<=2 is already satisfied with equality).

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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