# Solve the following system of inequalities graphically: 3x + 4 y ≤ 60, x + 3y ≤ 30, x ≥ 0, y ≥ 0

**Solution:**

3x + 4 y ≤ 60 ....(1)

x + 3y ≤ 30 ....(2)

The graph of the lines, 3x + 4 y = 60 and x + 3y = 30 , are drawn in the figure below.

Inequality 3x + 4 y ≤ 60 represents the region below the line, 3x + 4 y = 60 (including the line 3x + 4 y = 60).

Inequality x + 3y ≤ 30 represents the region the line, x + 3y = 30 (including the line x + 3y = 30).

Since x ≥ 0 and y ≥ 0 every point in the common shaded region in the first quadrant including the points on the respective line and the axes represents the solution of the given system of linear inequalities as follows:

NCERT Solutions Class 11 Maths Chapter 6 Exercise 6.3 Question 10

## Solve the following system of inequalities graphically: 3x + 4 y ≤ 60, x + 3y ≤ 30, x ≥ 0, y ≥ 0.

**Summary:**

Linear inequations 3x + 4 y ≤ 60, x + 3y ≤ 30, x ≥ 0, y ≥ 0 is given. We have found that the axes represents the solution of the given system of linear inequalities.