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Class 11MathematicsLinear InequalitiesGraphical solution of linear inequalities in two variablesHard
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For the line (3x+2y=18), which point lies in the half-plane (3x+2y \ge 18)?

Answer and explanation

Correct answer: ((5,2))

The direct answer is option C: (5,2) lies in the half-plane 3x + 2y ≥ 18. Test each point by substitution. For A, (2,3): 3(2) + 2(3) = 6 + 6 = 12, and 12 ≥ 18 is false. For B, (4,2): 12 + 4 = 16, so it is false. For C, (5,2): 15 + 4 = 19, and 19 ≥ 18 is true. For D, (1,5): 3 + 10 = 13, so it is false. Therefore only option C belongs to the required half-plane. The equality line 3x + 2y = 18 is the boundary; points on the side giving a value greater than 18 satisfy the inequality, and points giving a smaller value do not. Exam cue: for a proposed point, substitute first and compare directly.

Related tags

Point TestingHalf PlaneLinear Inequality
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10 more MCQs
  1. 1Which statement correctly means x∈[1,4]?
  2. 2Which statement is always true about the solution region of a system of linear inequalities in two variables?
  3. 3In the graph of the inequality (x+y\leq 4), where will the point ((0,0)) lie?
  4. 4For the inequality (y> x+1), how is the boundary line drawn?
  5. 5Which is the solution region of (y\leq 3)?
  6. 6What region does the graph of (x> -2) represent?
  7. 7What conclusion is obtained by testing ((0,0)) in (2x+y\geq 6)?
  8. 8Which statement is correct for the boundary line of (x+y<5)?
  9. 9For the inequality (x+2y\leq 8) with boundary (x+2y=8), which point is in the solution region?
  10. 10Will the boundary line be included in the graph of (y\geq -1)?
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