Linear Inequalities in Two Variables

Feasible region

The region of a graph that satisfies all the given inequalities at once.

EnglishFeasible region
Bahasa MelayuKawasan tersaur
中文可行区域

How it is used

For x ≥ 0, y ≥ 0 and x + y ≤ 6, the feasible region is the triangle with corners (0, 0), (6, 0) and (0, 6); the point (2, 3) lies inside because 2 + 3 = 5 ≤ 6.

Where it shows up in SPM

The goal of most Paper 2 questions in Linear Inequalities in Two Variables: you translate word conditions into inequalities, shade each one, and identify the region satisfying all of them. Questions then ask for integer points inside it, such as the maximum value of x + y that fits the constraints.

Don't confuse it with

Solution of an equationThe solution of two simultaneous equations is a single point; a feasible region is a whole area of points that satisfy several inequalities together.

Open the chapter: Linear Inequalities in Two Variables →

Frequently asked questions

How do I show the feasible region clearly when there are several inequalities?

Draw every boundary line first, then shade the unwanted side of each one lightly. The region left unshaded (or shaded by all, if the paper asks you to shade the wanted side) is the feasible region.

Label it R so the examiner sees exactly which area you mean.

Do points on the boundary count as part of the feasible region?

Only when that boundary comes from a ≤ or ≥ inequality, drawn as a solid line. If the boundary comes from a < or > inequality drawn dashed, points exactly on it are excluded, so an integer sitting on a dashed line does not satisfy the constraints.

Related terms

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