Question

Find the graphical solution of the following system of linear inequations:
3x + 2y ≤ 24, 3x + y ≥ 15, x ≥ 4

Answer 1

Writing the above inequalities as equations
3x + 2y ≤ 24

x	0	8
y	12	0
(x, y)	(0, 12)	(8, 0)

3x + y ≥ 15

x	0	5
y	15	0
(x, y)	(0, 15)	(5, 0)

x ≥ 4

x	4	4
y	0	1
(x, y)	(4, 0)	(4, 1)

The inequality 3x + 2y ≤ 24 represents the region below the line including the points on the line 3x + 2y = 24.
The inequality 3x + y ≥ 15 represents the region above the line, including the points on the line 3x + y = 15.
The inequality x ≥ 4 repyesents the region to the right of the line, including the points on the line x = 4.
∴ The shaded region between the lines represents the solution of the given inequality.