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Class 11MathematicsLinear InequalitiesGraphical solution of linear inequalities in two variablesEasy
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What does testing \((3,2)\) in \(3x+y\leq 9\) show?

Answer and explanation

Correct answer: it is not in solution

Substituting \((3,2)\) gives \(3(3)+2=11\). Since \(11\leq 9\) is false, the point is not in the solution set of the inequality. It is not on the boundary either, because a boundary point must satisfy \(3x+y=9\). Exam tip: Test a point by substituting its \(x\)- and \(y\)-coordinates into the inequality and checking whether the statement is true.

Related tags

Linear InequalitiesPoint TestGraphical SolutionBoundary LineCoordinate PlaneGraphical Solution Of Linear Inequalities In Two VariablesMathematicsClass 11 Mcq
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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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