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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 2 · 25 questions

TOPIC PRACTICE

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25 questions

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  1. ((0,0))
  2. ((4,0))
  3. ((2,2))
  4. ((0,4))
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  1. (y \ge 2x-3)
  2. (y>2x-3)
  3. (y \le 2x-3)
  4. (y<2x-3)
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  1. ((5,0))
  2. ((0,5))
  3. \(\left(\frac{10}{3},\frac{10}{3}\right)\)
  4. ((0,0))
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  1. ((0,0))
  2. ((6,0))
  3. ((0,3))
  4. ((2,3))
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  1. (x \ge 0), (y \ge 0), (x+y \le 5)
  2. (x \ge 1), (x \le 5), (y \ge 2), (y \le 6)
  3. (x+y \ge 4), (x+y \le 8)
  4. (y \ge x), (y \le x+3)
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  1. This point is in the solution region
  2. This point is on the boundary line
  3. This point is not in the solution region
  4. This point is in every half-plane
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  1. (y \ge x) and (y \le -x+6)
  2. (y \le x) and (y \ge -x+6)
  3. (y \ge x) and (y \ge -x+6)
  4. (y \le x) and (y \le -x+6)
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  1. ((2,7))
  2. ((1,8))
  3. ((6,4))
  4. ((5,5))
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  1. Origin is outside because (0>0) is false
  2. Origin is on boundary and included in solution
  3. Origin is on boundary but not in solution
  4. Origin is included only when line is dotted
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  1. (3x-y \le 9)
  2. (3x-y<9)
  3. (3x-y \ge 9)
  4. (3x-y>9)
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  1. (2)
  2. (3)
  3. (4)
  4. (5)
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  1. (3)
  2. (4)
  3. (6)
  4. (12)
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  1. ((4,4))
  2. ((8,2))
  3. ((2,3))
  4. ((0,6))
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  1. ((2,1))
  2. ((3,2))
  3. ((1,2))
  4. ((4,0))
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  1. \((0,4)\)
  2. \((16,0)\)
  3. \((4,0)\)
  4. \((0,16)\)
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  1. (x \le 3)
  2. (x \ge 3)
  3. (0 \le x \le 3)
  4. (x=6)
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  1. Closed strip between two parallel lines
  2. Triangle between intersecting lines
  3. Empty region
  4. Entire plane
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  1. Bounded triangle
  2. Cut part of an unbounded strip
  3. Empty region
  4. Only one point
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  1. ((0,0))
  2. ((1,-3))
  3. ((3,1))
  4. ((2,4))
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  1. (x-3y \le 6)
  2. (x-3y<6)
  3. (x-3y \ge 6)
  4. (x-3y>6)
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  1. (3)
  2. (4)
  3. (5)
  4. (6)
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  1. Their common solution is the line (x+y=5)
  2. Their common solution is empty
  3. Together they cover the entire plane
  4. They form a closed strip
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  1. (2)
  2. (3)
  3. (4)
  4. (6)
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  1. \(\left(\frac{22}{5},\frac{24}{5}\right)\)
  2. \(\left(\frac{24}{5},\frac{22}{5}\right)\)
  3. ((4,5))
  4. ((5,4))
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  1. Point ((0,4))
  2. Point \(\left(\frac{8}{3},\frac{8}{3}\right)\)
  3. Point ((4,0))
  4. Point ((8,8))

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