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📐 Mathematics  ·  Linear Inequalities  ·  JEE

Two linear inequalities 3x + 4y <= 24 and x + y <= 7 (with x, y >= 0) are graphed together. What are the coordinates of their boundary lines' intersection point?

Answer: (4, 3).

  • A (4, 3)
  • B (3, 4)
  • C (8, 0)
  • D (0, 6)

Correct answer: A. (4, 3)

Explanation: Solve 3x+4y=24 and x+y=7 together: from the second, y=7-x. Substitute: 3x+4(7-x)=24, 3x+28-4x=24, -x=-4, x=4, y=3. Intersection: (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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