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Class 11MathematicsLinear InequalitiesGraphical solution of linear inequalities in two variablesEasy
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Is \((0,5)\) a solution of \(2x+5y\leq 20\)?

Answer and explanation

Correct answer: No

Substituting \((0,5)\) gives \(2x+5y=2(0)+5(5)=25\). Since \(25\leq20\) is false, the point is not a solution of the inequality. A point lies on the boundary line only when the value is exactly \(20\), but here it is \(25\). Exam tip: test a point by directly substituting its \(x\)- and \(y\)-coordinates into the inequality.

Related tags

Linear InequalitiesPoint TestGraphical SolutionBoundary LineTwo VariablesGraphical 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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