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📐 Mathematics  ·  Linear Inequalities  ·  JEE

Solve the system graphically: x + y >= 4 and x + y <= 8 (with x, y >= 0). The feasible region lies:

Answer: Between the two parallel boundary lines, in the first quadrant.

  • A Mostly outside both boundary lines, away from the bounded strip
  • B Between the two parallel boundary lines, in the first quadrant
  • C Just on the line x + y = 4, treating it as an equality constraint alone
  • D Just on the line x + y = 8, treating it as an equality constraint alone

Correct answer: B. Between the two parallel boundary lines, in the first quadrant

Explanation: The region satisfying both x+y>=4 and x+y<=8 in the first quadrant is the band between the two parallel lines x+y=4 and x+y=8.

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 →