Question

Solve 3x – 6 >= 0 graphically in
two dimensional plane.​

Answer 1

Answer:

(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.