The linear inequations for which the shaded area in the following figure is the solution set, are

Question

The linear inequations for which the shaded area in the following figure is the solution set, are (A) x+y ≤ 1, 2 x +y ≥ 2, x-2 y ≥ 8, x ≤ 0, y ≥ 0 (B) x-y ≥ 1, 2 x +y ≥ 2, x+2 y ≥ 8, x ≥ 0, y ≥ 0 (C) x-y ≤ 1, 2 x +y ≥ 2, x+2 y ≤ 8, x ≥ 0, y ≥ 0 (D) x+y ≥ 1, 2 x +y ≤ 2, x+2 y ≥ 8, x ≥ 0, y ≥ 0

Tardigrade Admin · Accepted Answer

Let L1: x+2 y=8; L 2 2 x + y =2 L 3: x - y =1 ince the shaded area is below the line L 1, we have x+2 y ≤ 8. Since the shaded area is above the line L2, we have 2 x +y ≥ 2. Since the common region is to the left of the line L 3, we have x - y ≤ 1

Q. The linear inequations for which the shaded area in the following figure is the solution set, are

$x + y \leq 1, 2 x + y \geq 2, x - 2 y \geq 8, x \leq 0, y \geq 0$

$x - y \geq 1, 2 x + y \geq 2, x + 2 y \geq 8, x \geq 0, y \geq 0$

$x - y \leq 1, 2 x + y \geq 2, x + 2 y \leq 8, x \geq 0, y \geq 0$

$x + y \geq 1, 2 x + y \leq 2, x + 2 y \geq 8, x \geq 0, y \geq 0$

Q. The linear inequations for which the shaded area in the following figure is the solution set, are

x+y≤1,2x+y≥2,x−2y≥8,x≤0,y≥0

x−y≥1,2x+y≥2,x+2y≥8,x≥0,y≥0

x−y≤1,2x+y≥2,x+2y≤8,x≥0,y≥0

x+y≥1,2x+y≤2,x+2y≥8,x≥0,y≥0

Let L1​:x+2y=8; L2​2x+y=2 L3​:x−y=1 ince the shaded area is below the line L1​, we have x+2y≤8. Since the shaded area is above the line L2​, we have 2x+y≥2. Since the common region is to the left of the line L3​, we have x−y≤1

$x + y \leq 1, 2 x + y \geq 2, x - 2 y \geq 8, x \leq 0, y \geq 0$

$x - y \geq 1, 2 x + y \geq 2, x + 2 y \geq 8, x \geq 0, y \geq 0$

$x - y \leq 1, 2 x + y \geq 2, x + 2 y \leq 8, x \geq 0, y \geq 0$

$x + y \geq 1, 2 x + y \leq 2, x + 2 y \geq 8, x \geq 0, y \geq 0$