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In the first quadrant, what is the \(x\)-intercept of the region formed by \(4x+y\le 20\)?

Answer and explanation

Correct answer: \((5,0)\)

To find the \(x\)-intercept, use the boundary line \(4x+y=20\) and put \(y=0\). This gives \(4x=20\), so \(x=5\). Hence, the \(x\)-intercept is \((5,0)\). The point \((0,5)\) lies on the \(y\)-axis, so it is not an \(x\)-intercept. Exam tip: for an \(x\)-intercept, always set \(y=0\).

Related tags

Linear InequalitiesGraphical SolutionX-InterceptFirst QuadrantClass 11 MathematicsGraphical Solution Of Linear Inequalities In Two VariablesMathematicsClass 11 Mcq

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