Exhibit graphically the solution set of the linear inequations

x + y ≤ 5, 4x + y ≥ 4, x + 5y ≥ 5, x ≤ 4, y ≤ 3

Converting the inequations into equations, we obtain:

x + y = 5,    4x + y = 4,    5x + y = 5

Region represented by: The line x + y = 5 meets the coordinate axes at A(5, 0) and B(0, 5) respectively. Join these points by a thick line. Clearly, (0, 0) satisfies the inequality x + y < 5. So, the portion containing the origin represents the solution set of the inequation x + y < 5.

Region represented by: The line 4x + y = 4 meets the coordinate axes at A₁(1, 0) and B₁(0, 4) respectively. Join these points by a thick line. Clearly, (0, 0) does not satisfy the inequation 4x + y > 4.

Region represented by: The line 5x + y = 5 meets the coordinate axes at A₂(1, 0) and B₂(0, 5) respectively. Join these two points by a thick line. We find that (0, 0) does not satisfy the inequation 5x + y > 5. So, the portion not containing the origin is represented by the given inequation.

The common region of the above five regions represents the solution of the given linear constaints as shown in fig. 

Solve the following system of inequalities graphically.