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📐 Mathematics  ·  Linear Inequalities  ·  JEE

For the inequality x + y <= 5 with x >= 0, y >= 0, what shape is the feasible region?

Answer: A triangle with vertices (0,0), (5,0), (0,5).

  • A An unbounded strip extending infinitely along the line x + y = 5
  • B A triangle with vertices (0,0), (5,0), (0,5)
  • C A circle of radius 5 centred at the origin
  • D A single line segment joining (5,0) and (0,5)

Correct answer: B. A triangle with vertices (0,0), (5,0), (0,5)

Explanation: The constraints x>=0, y>=0, x+y<=5 bound a triangular region with corners at the origin and the two intercepts (5,0) and (0,5).

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.

Read the full Linear Inequalities notes →