Solve the following system of inequalities graphically: x - 2 y ≤ 3, 3x + 4 y ≥ 12, x ≥ 0, y ≥ 1

Solution:

x - 2 y ≤ 3 ....(1)

3x + 4 y ≥ 12 ....(2)

y ≥ 1 ....(3)

x ≥ 0 ....(4)

The graphs of the lines, x - 2y = 3 , 3x + 4 y = 12 and y = 1 are drawn in the figure below.

Inequality x - 2 y ≤ 3 represents the region above the line, x - 2 y = 3 (including the line).

Inequality 3x + 4 y ≥ 12 represents region above the line, 3x + 4 y = 12 (including the line).

Inequality y ≥ 1 represents the region above the line, y = 1 (including the line).

Inequality x ≥ 0 represents the region on the right and side of the y-axis (including the y-axis).

Hence, the solution of the given system of linear inequalities is represented by the common shaded region including the points on the respective lines and y-axis as follows:

NCERT Solutions Class 11 Maths Chapter 6 Exercise 6.3 Question 12

Solve the following system of inequalities graphically: x - 2 y ≤ 3, 3x + 4 y ≥ 12, x ≥ 0, y ≥ 1

Summary:

Linear inequations x - 2 y ≤ 3, 3x + 4 y ≥ 12, x ≥ 0, y ≥ 1 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 and y-axis