Question

Which system of inequalities is represented by the graph? ⎧⎩⎨⎪⎪y<−12x+2y≤2x−1y≥−4 ⎧⎩⎨⎪⎪y>−12x+2y≥2x−1y≥−4 ⎧⎩⎨⎪⎪y>−2x+2y≥12x−1y≥−4 ⎧⎩⎨⎪⎪y<−2x+2y≤12x−1y≥−4

Answer 1

Answer: D

Explanation:

Let say a: the line decreasing

b: the line increasing

`a: \ is\ passing\ through\ (0,2)\ and\ (2,-2)\\has \ the \ slope=(2+2)/(0-2) =-2\\its\ equation\ is\ y-2=-2(x-0) \ or\ y=-2x+2\ or\ 2x+y-2=0 \\for\ (0,0): -2 <=0\\\\\boxed{First\ region\ is\ y\leq -2x+2}\\\\`

`b:\ is\ passing\ through\ (2,0)\ and\ (-2,-2) \\has\ the\ slope \ = \frac{-2-0} {-2-2} =\frac{1} {2} \\its\ equation\ is\ y-0=(1)/(2)(x-2)\ or\ y=(x)/(2)-1 \ or\ -x+2y+2=0\\for\ (0,0):\ +2 > 0\\\\\boxed{Second \ region\ is\ y\leq (x)/(2)-1 }\\`

Answer is D