Answer:
The system of linear inequalities is
![y\geq x+1](https://tex.z-dn.net/?f=y%5Cgeq%20x%2B1)
![y>-x-2](https://tex.z-dn.net/?f=y%3E-x-2)
Step-by-step explanation:
From the given graph it is noticed that we have two lines one is solid and second is dashed.
The solid line passing through the points (0,1) and (-1,0). The dashed line passing through the points (0,-2) and (-2,0).
If line passing through two points, then the equation of line is
![y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%28x-x_1%29)
The related equation of solid line is
![y-1=\frac{0-1}{-1-0}(x-0)](https://tex.z-dn.net/?f=y-1%3D%5Cfrac%7B0-1%7D%7B-1-0%7D%28x-0%29)
![y=x+1](https://tex.z-dn.net/?f=y%3Dx%2B1)
Similarly the related equation of dashed line is
![y-(-2)=\frac{0-(-2)}{-2-0}(x-0)](https://tex.z-dn.net/?f=y-%28-2%29%3D%5Cfrac%7B0-%28-2%29%7D%7B-2-0%7D%28x-0%29)
![y=-x-2](https://tex.z-dn.net/?f=y%3D-x-2)
From the given figure it is noticed that the point (0,2) is in the shaded region, it means the point (0,2) will satisfy the inequalities.
![2=0+1](https://tex.z-dn.net/?f=2%3D0%2B1)
![2=1](https://tex.z-dn.net/?f=2%3D1)
This statement will true if the sign of inequality is
because It is a solid line.
![2=-0-2](https://tex.z-dn.net/?f=2%3D-0-2)
![2=-2](https://tex.z-dn.net/?f=2%3D-2)
This statement will true if the sign of inequality is > because It is a dashed line.
The system of linear inequalities is
![y\geq x+1](https://tex.z-dn.net/?f=y%5Cgeq%20x%2B1)
![y>-x-2](https://tex.z-dn.net/?f=y%3E-x-2)