Mathematics

Graphical solution of linear inequalities in two variables

In this Class 11 Mathematics topic from the chapter Linear Inequalities, students learn how to represent a linear inequality in two variables on the Cartesian plane. They study how to draw the boundary line, decide whether it is included or excluded, and identify the correct half-plane by testing a point. The topic also explains how multiple inequalities can be represented together to find their common feasible region, helping students interpret solutions visually and connect algebraic conditions with graphs.

Hard · Level 7 · 1 questions

Practice questions

01For the solution region 2x+y ≤ 12, x+2y ≤ 12, x ≥ 0, y ≥ 0, what is the maximum value of x+y?

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Answer and explanation

Correct answer: B. 8

The feasible region is bounded by two lines and the coordinate axes, so a linear objective such as x + y reaches its maximum at a corner point. The boundary lines 2x + y = 12 and x + 2y = 12 intersect by subtraction: x − y = 0, hence x = y; substituting gives 3x = 12, so the intersection is (4, 4). The feasible vertices are (0, 0), (6, 0), (4, 4), and (0, 6). Evaluating x + y gives 0, 6, 8, and 6 respectively. Therefore the maximum value is 8 at (4, 4), so option B is correct. Values 10 and 12 exceed the feasible corner values and cannot be attained in the region.

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Graphical solution of linear inequalities in two variables

Practice questions

01For the solution region 2x+y ≤ 12, x+2y ≤ 12, x ≥ 0, y ≥ 0, what is the maximum value of x+y?हल-क्षेत्र 2x+y ≤ 12, x+2y ≤ 12, x ≥ 0 और y ≥ 0 के लिए x+y का अधिकतम मान क्या है?

Analytics choices

01For the solution region 2x+y ≤ 12, x+2y ≤ 12, x ≥ 0, y ≥ 0, what is the maximum value of x+y?