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Solve the following system of inequalities graphically: 2x + y ≥ 4, x + y ≤ 3, 2x - 3y ≤ 6
Solution:
2x + y ≥ 4 ....(1)
x + y ≤ 3 ....(2)
2x - 3y ≤ 6 ....(3)
The graph of the lines, 2x + y = 4, x + y = 3 and 2x - 3y = 6 , are drawn in the figure below.
Inequality 2x + y ≥ 4 represents the region above the line, 2x + y = 4 (including the line).
Inequality x + y ≤ 3 represents the region below the line, x + y = 3 (including the line).
Inequality 2x - 3y ≤ 6 represents the region above the line, 2x - 3y = 6 (including the line).
Hence, the solution of the given system of linear inequalities is represented by the common shaded region including the points on the respective lines as follows:
NCERT Solutions Class 11 Maths Chapter 6 Exercise 6.3 Question 11
Solve the following system of inequalities graphically: 2x + y ≥ 4, x + y ≤ 3, 2x - 3y ≤ 6.
Summary:
Linear inequations 2x + y ≥ 4, x + y ≤ 3, 2x - 3y ≤ 6 is given. We have found that the solution of the given system of linear inequalities is represented by the common shaded region including the points on the respective lines
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