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📐 Mathematics  ·  Linear Inequalities  ·  JEE

For the system 3x + 2y <= 18, x + 2y <= 10, x >= 0, y >= 0, what are the coordinates of the corner point where both boundary lines intersect (away from the axes)?

Answer: (4, 3).

  • A (4, 3)
  • B (3, 4)
  • C (6, 0)
  • D (0, 5)

Correct answer: A. (4, 3)

Explanation: Subtracting x + 2y = 10 from 3x + 2y = 18 gives 2x = 8, so x = 4. Then 4 + 2y = 10 gives y = 3. The intersection point is (4, 3).

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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