(i) 3x- 6 ≥ 0 ………………..(1)
Draw the graph of 3x -6 = 0 i.e., x = 2 by thick line
Put x = 0 in (1), we get - 6 > 0 which is false.
∴ Solution region does not contains the origin
The shaded region is the solution region,
(ii) 2x + y >6 …………………..(1)
Draw the graph of 2x + y = 6 by thick line. It passes through (3, 0) and (0, 6). Join these points, put x = 0 and y = 0 in (1), we get 0 + 0 > 6 which is false.
∴ Solution region does not contain the origin
(iii) 3x + 4y < 12 …………… (1)
Draw the graph of 3x + 4y = 12 by thick line. It passes through (4, 0) and (0, 3). Join these points, put x = 0 and y = 0 in (1), we get 0 + 0 ≤ 12 which is true.
∴ The solution region contains the origin
∴ The shaded region is the solution region,
(iv) y + 8 ≥2x ………… (1)
Draw the graph of y+8 = 2 by thick line It passes through (4, 0) and (0, -8) Join these points, put x = 0 and y = 0 in (1), we get 0+8≤0 which is true.
∴ The solution region contains the origin
∴ The shaded region is the solution region,
(v) x – y ≤ 2 ………… (1)
Draw the graph of x – y ≤ 2 by thick line It passes through (2, 0) and (0, -2) Join these points, put x = 0 and y = 0 in (1), we get 0 – 0 < 2 which is true.
∴ The solution region contains the origin
∴ The shaded region is the solution region.
(vi) -3x + 2y>-6 ………… (1)
Draw a graph of -3x + 2y = -6 by thick line. It passes through (2, 0) and (0, -3) Join these points, put x = 0 and y = 0 in (1), we get 0 + 0 > -6 which is true.
∴ The solution region contains the origin
∴ The shaded region is the solution region.
