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What is the position of \((4,0)\) in the graph of \(3x+y\le 9\)?

Answer and explanation

Correct answer: outside solution region

Substituting \((4,0)\) into \(3x+y\le 9\) gives \(3(4)+0=12\). Since \(12\le 9\) is false, the point lies outside the solution region. A point would lie on the boundary only if \(3x+y=9\), which is not true here. Exam tip: test a point by substituting its coordinates into the inequality.

Related tags

Linear InequalitiesPoint TestSolution RegionGraphical InequalitiesClass 11Graphical Solution Of Linear Inequalities In Two VariablesMathematicsClass 11 Mcq

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