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📐 Mathematics  ·  Linear Inequalities  ·  JEE

Which point satisfies both x - y <= 2 and x + y <= 6 (along with x,y >= 0)?

Answer: (2, 2).

  • A (5, 5)
  • B (2, 2)
  • C (6, 0)
  • D (0, 8)

Correct answer: B. (2, 2)

Explanation: At (2,2): x-y=0<=2 true, x+y=4<=6 true. Both satisfied. Check (5,5): x+y=10>6 fails.

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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