Question

Solve the following systems of inequalities graphically x + y ≥ 1 , 3x + 4y < 12 , x - 2y ≤ 2 , x ≥ 0 , y ≥ 0 .

Answer 1

x – 2y ≤ 3 …………………………. (1)

3x + 4y ≥ 12 ……………….…… (2)

y ≥ 1 …………………………………. (3)

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

Inequality (1) represents the region above the line, x – 2y = 3 (including the line x – 2y = 3).

Inequality (2) represents the region above the line, 3x + 4y = 12 (including the line 3x + 4y = 12).

Inequality (3) represents the region above the line, y = 1 (including the line y = 1).

The inequality, x ≥ 0, represents the region on the right hand side of y-axis (including 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.