Given:
The graph of the system of inequalities.
To find:
The system of inequalities.
Solution:
From the given graph it is clear that the first line passes through the points (0,2) and (1,-1). So, the equation of the boundary line is:
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-2=\dfrac{-1-2}{1-0}(x-0)[/tex]
[tex]y-2=-3x[/tex]
[tex]y=-3x+2[/tex]
The shaded region lies above the line and the boundary line is a solid line. So, the sign of inequality must by ≥.
[tex]y\geq -3x+2[/tex]
The second line passes through the points (0,-2) and (3,0). So, the equation of the boundary line is:
[tex]y-(-2)=\dfrac{0-(-2)}{3-0}(x-0)[/tex]
[tex]y+2=\dfrac{2}{3}x[/tex]
[tex]y=\dfrac{2}{3}x-2[/tex]
The shaded region lies above the line and the boundary line is a solid line. So, the sign of inequality must by ≥.
[tex]y\geq \dfrac{2}{3}x-2[/tex]
Therefore, the system of inequalities contains two linear inequalities [tex]y\geq -3x+2[/tex] and [tex]y\geq \dfrac{2}{3}x-2[/tex].
