Solve graohically the system of inequalities x + 2y ≥ 20, 3x + y ≤ 15
x + 2y = 20 … (1) and 3x + y = 15 ….(2)
(i). Region represented by x + 2y ≥ 20 :
line (1) meets x-axis it (20,0) and y-axis at (0, 10) By joining these two points we get the line (1) put x = 0, y = 0 in x + 2y ≥ 20 ⇒ 0 ≥ 20, which is not true
∴ (0,0) does not satisfy the in equation
∴ The portion which does not contain origin represents the solution set of x + 2y ≥ 20
(ii) Region represented by 3x + y ≤ 15 line (2) meets x-axis at (5,0) and y-axis at (0, 15) By joining these two, we get line (2)
∴ put x = 0, y = 0 in 3x + y ≤ 15 ⇒ 0 ≤ 15 which is true
∴ (0, 0) satisfies the in equation
∴ The portion containing the origin represent the solution set of 3x + y = 15
∴ All the points in the common shaded region are the solutions of the system of linear in equations
