In order find the Inequalities, First we need to Find the Equations of Both the Lines.
Equation of First line :
It is passing through the Points (0 , 2) and (4 , 0)
⇒ Slope = [tex]\frac{2 - 0}{0 - 4} = \frac{-2}{4} = \frac{-1}{2}[/tex]
⇒ Equation of the First Line : [tex]y - 2 = \frac{-1}{2}(x)[/tex]
⇒ Equation of the First Line : x + 2y = 4
Equation of Second Line :
It is passing through the Points (1.5 , 0) and (0 , -3)
⇒ Slope = [tex]\frac{0 + 3}{1.5 - 0} = \frac{3}{1.5} = 2[/tex]
⇒ Equation of the Second Line : y + 3 = 2x
⇒ Equation of the Second Line : 2x - y = 3
As the Shaded Area of the First Line is away from the Origin :
⇒ x + 2y ≥ 4
As the Shaded Area of the Second Line is towards the Origin and it is a Dotted line :
⇒ 2x - y < 3
So, the System of Linear Inequalities are :
⇒ x + 2y ≥ 4
⇒ 2x - y < 3
